The comments, made in a wide-ranging interview with the BBC, come after a summer in which the United boss’ relationships with his players have come under intense scrutiny, especially amid speculation of a fractured relationship with star player Paul Pogba.
But Lukaku paints a different picture, questioning the media portrayal of Mourinho.
“People know a side from him which is he’s a winner,” said Lukaku.
“But what I like about him is he’s not going to fake his emotions. When he’s mad, you know he is mad. When he’s happy, you see he is happy.
“I don’t understand why people don’t like the realness about him. When he’s mad at me I know he is mad at me, and I try to do what he wants so he is happy again.”
Lukaku, 25, went on to say that far from there being a tense relationship between Mourinho and the squad, the manager is a “real family guy” who “makes the players laugh”.
“My relationship with him is cool,” the striker said.
“He makes me laugh, he makes the players laugh, he’s a real family guy. He fights for his players, but he’s real. When you’re not happy, you don’t need to fake your emotions.
“People need to appreciate that, at least there are people who are real in this world like him. Because most of the managers in the league, when they are not happy they try to find a way to seem happy.
“You should respect that he wants to keep his own personality and not shy away from confrontation. Here, he really wants us to improve. He is a normal guy, we get along well. He is cool with everybody.”
The Belgian conceded that modern-day footballers may not fully appreciate Mourinho’s direct style, adding that his generation of players may have gotten “soft” compared to the previous era.
“Sometimes footballers, we get soft a little bit,” he said. “If I listen to players from back in the day and now, a manager cannot say what he wants to a player because you feel attacked.
“But I don’t feel attacked, because that’s who I am – I am a tough man, but that doesn’t come from football, that comes from my background.”
Rashford has started only one club game so far this term, before impressing for Gareth Southgate’s England by starting and scoring against both Spain and Switzerland.
Those performances led to questions around Rashford’s playing time at United, with former Liverpool defender Jamie Carragher saying he needs to leave if he ever wants to develop into a world-class striker.
Such analysis has clearly got under Mourinho’s skin, with the boss giving a 276-second answer to one question about the forward’s performances for England.
“I think I can expect that Sunday I’m going to be highly criticised for not playing him because some of the boys are really obsessed with me and some of them, they have I think a problem with some compulsive lies,” the United boss said of Rashford, who starts a three-match suspension at Watford.
“So I can expect that Sunday some of them they will wake up in the morning and, as always, the first thing they think, that comes to their mind, is Jose Mourinho, so I can imagine on Sunday I am going to be criticised for not playing Marcus.
“But it is not my fault, he is suspended, so probably you should remind them that he is suspended, and he cannot play.
“Performances with England, of course I’m happy. He played well, he competed well, he scored and especially in a period where he comes with some sadness after his suspension and it was very good that he did that.
“If you don’t mind to lose a couple of minutes with me, I’m going to do something, not for you but for the United fans, because I think I hold myself to the United fans and for them I am going to spend two minutes with you.”
At this point Mourinho read from a hand-written note to reel off Rashford’s matches, overall minutes and average number of 90 minutes for the previous two campaigns.
“Marcus Rashford is not Dominic Solanke, he’s not Ruben Loftus-Cheek , he’s not Dominic Calvert-Lewin,” he concluded, taking aim at some of United’s rivals.
“He’s Marcus Rashford, Manchester United player, with an incredible number of appearances and an incredible number of minutes played at the highest level in the best possible competitions.
“So Manchester United supporters – for you and just for you – to know what we are doing with Marcus Rashford, Luke Shaw, Jesse Lingard, Scott McTominay, that’s what we are doing here.”
More on @MarcusRashford: "With me [as manager] in two seasons, he's had 105 appearances, 5,744 minutes, 63.7 matches of 90 minutes, including five finals. An incredible number of appearances at the highest level." #MUFC— Manchester United (@ManUtd) September 14, 2018
Mourinho was pointed with his remarks and clearly irritated by the perception he does not play Rashford enough.
“It’s not a perception,” he retorted. “You know some of the persons, everybody knows that they have double salaries.
“They work also for the clubs and when they work also for the clubs of course they are not independent and of course they conduct things in the direction they want to conduct things.
“That’s obvious and that’s human, and that’s natural. It’s not ethical but I accept, clearly.
“The ones that wake up in the morning and the first thing that comes into their mind is Jose Mourinho and Manchester United, I feel sorry for them because there are much more interesting things to wake up and to be happy in the morning (about) than to speak immediately about us and about football.
“But for the Manchester United supporters, I think it is important they have the right idea of how things are in reality.
“But the most important thing of all is that the kid is a good kid, the kid is a good player, he knows what Manchester United did for him.
“Starting in the academy, then Mr (Louis) Van Gaal’s support, then my support and the club’s support, and the new contract and the new shirt, and being selected for every single match since I am here.
“Marcus Rashford was selected for every single match – he was never, never one day out of selection because of my decision, only if injured or, like in this, because he is suspended.
“He was never, never out of a selection, so he knows and that’s the most important thing.
“But, again, media is very important, and I think it’s very important the Manchester United supporters they know the truth. That’s why I’m going so specific about his numbers.”
Andrea Berta is reportedly being lined up to become the new director of football at Manchester United.
Chief Executive Ed Woodward is planning a major restructuring behind the scenes at Old Trafford, with the Italian transfer guru considered high on the club’s priority list.
But just who is the man United are targeting?
Here’s a quick fact file on the Atletico Madrid sporting director.
Oversaw Atletico’s rise
The Italian joined Atletico Madrid from Serie A side Genoa in 2013, having previously worked at Parma as well.
When Berta joined the club, Radamel Falcao signed for Monaco for a mammoth €60million fee, with Diego Costa coming to the fore for Los Rojiblancos that season. David Villa, Jose Gimenez, and Toby Alderweireld were among the major signings in that summer transfer window.
At the end of the season, Atletico were La Liga champions for the first time in 18 years.
Since then, they’ve reached two Champions League finals and won the Europa League. In that time, Berta has risen from scout to technical director to overall sporting director, in charge not just of player recruitment but all first-team operations.
It’s safe to say he’s presided over the most successful period in club history.
Under Berta, Atletico have made a habit of unearthing gems and turning handsome profits. Alderweireld, Diego Costa, Arda Turan and Jackson Martinez are among the players sold in big-money moves during Berta’s time at the Wanda Metropolitano.
But what’s most impressive is his record as a recruiter. He was responsible for the signings of Antoine Griezmann and Jan Oblak in 2014 when they were signed for €30million and €16million respectively. The Italian also oversaw the return of Costa, as well as a stunning summer 2018 window in which Griezmann and Diego Godin were tied down to new contracts and Rodri, Thomas Lemar, Nikola Kalinic and Gelson Martins were among the new players recruited.
What would United get?
Berta is one name in a small shortlist of candidates being reported on as a potential director of football at United. The club are looking to restructure their entire top-level football set-up, in order to streamline recruitment and transfers.
The Atletico director may be the perfect man for the job at Old Trafford. He has a reputation in Europe for being among the continent’s better talent-spotters, as well as for his ability to get a deal over the line.
Plus, having worked exclusively with Diego Simeone as manager, Berta will understand the idea of establishing a footballing philosophy and recruiting players who fit that. Whether that would put him at odds with Jose Mourinho wold have to be seen. Mourinho has a rigid footballing system that doesn’t quite match with the club’s overall philosophy, which may cause clashes sometimes. But then, that’s part and parcel of the job – especially when working with the Portuguese.