The 26-year-old ended his two-season stint at Old Trafford on Thursday, joining Inter Milan in an 80 million euros (£73.75million) deal.
Lukaku’s exit became rather unsavoury as he started the week training with boyhood club Anderlecht and Solskjaer is happy to see the striker leave.
“It was time now for Rom to go because I think we got a good deal, he’s happy, so I think both parties ended that deal as it should be,” he said.
“Rom was injured for a while this pre-season, he didn’t participate, so I just hope for him that he’ll get a good start at Inter Milan.”
Solskjaer is confident United’s attack will do well despite losing the option of a regular goalscorer.
“Towards the end of last season, we didn’t score a lot of goals, did we?” he said.
“And you do have players that you think will have an impact and Mason Greenwood’s pathway would have been a lot more difficult, of course if we had another forward there.
“For me, I believe Mason is going to be playing and involved a lot and when he is, he’ll score goals.”
While Lukaku followed Ander Herrera and Antonio Valencia in making summer exits, only Harry Maguire, Aaron Wan-Bissaka and Daniel James arrived.
PA understands Solskjaer was also looking to improve in central midfield and on the right wing, but the United manager seemed happy enough.
“Do you know, I think when the transfer window closes it’s that great feeling of relief,” the Norwegian said ahead of Sunday’s match against Chelsea.
“Now it’s done, now we know we’re looking forward with and I’m delighted with the three we’ve signed.
“Well, that’s (negativity) not the feeling inside the club anyway and the feeling with the fans I’ve met, they are excited with the ones we’ve had.
“Of course, there is always going to be fans out there wanting to sign players. That’s just part and parcel of being here. The players are here now, they’ve been shown that trust and we believe in them.”
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The German midfielder, who had just entered the final year of his previous deal, is now committed to the club until 2023.
The news ends speculation over the future of the 28-year-old, who joined City from Borussia Dortmund in 2016.
Gundogan told the club’s website, www.mancity.com: “I am very happy to have signed the new contract. I have hugely enjoyed the last three years here at City and everyone at the club has helped make me feel at home from my very first day.
“It’s a privilege to be a part of this team, playing the style of football we do and winning trophies. It’s very difficult to do that and I’m delighted to be a part of it.
“I’m really excited about what we can go on to achieve in the next few seasons.”
Gundogan’s first season at City was cut short by a serious knee injury but he has been a key part of the club’s back-to-back Premier League triumphs over the past two campaigns.
The deal comes in the week City bolstered their squad with the signings of Joao Cancelo and Scott Carson.
Director of football Txiki Begiristain said: “Ilkay’s new deal is more excellent news for our club.
“He has shown how important he is to the team and has played a huge part in everything that we have achieved so far.
“We are thrilled he has committed his long-term future to Manchester City.”
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Having amassed as much as 198 points in consecutive Premier League seasons, the scope for improvement in squad depth was not high for Pep Guardiola heading into the new season. But, nevertheless, Manchester City have strengthened their glittering side with some marquee signings.
Rodri, Joao Cancelo and Angelino were signed from Atletico Madrid, Juventus and PSV Eindhoven respectively, while Danilo and Fabian Delph were among the big names departing the Etihad Stadium.
Ahead of their opening match against West Ham on Saturday, we take a look at the new, improved City squad that will be bidding to clinch a third successive league title.
GOALKEEPERS – B+
In Ederson, the Sky Blues have a well-rounded keeper who is great with his feet and solid with his hands. He has proved to be an astute purchase, having integrated the team’s style of play effectively over the past two title-winning seasons.
Back-up keeper Claudio Bravo, 36, has established himself as a specialist in domestic cup games, especially when penalty shoot-outs are on the menu. However, the Chilean has rarely been preferred in league matches, after a series of blunders in his maiden season.
While Bravo can be relied upon to take City through in a crucial FA Cup tie, a long-term injury for Ederson could shake things up in the league. Derby County custodian Scott Carson was roped in on loan on deadline day but there is not much clarity as to what Guardiola has in mind for the new-signing.
DEFENCE – B
It would not be a stretch to suggest that City have the second-best defence in the league, with Liverpool stepping highest on the podium.
The Aymeric Laporte-John Stones centre-back pairing has been solid, bar the rare loss of concentration that is generally dealt with by the reliable Ederson. The pair have developed a great sense of chemistry that can only develop over time.
However, the lack of depth in central defence could come back to bite the Premier League champions during the business end of the campaign.
Nicolas Otamendi and Eliaquim Mangala could have formed a solid partnership back in 2015/16 but both players have experienced a steady decline ever since. The Sky Blues should have scanned the market for a better third/fourth choice centre-back during the summer but opted against it.
The full-back positions are well-decorated with big names and talented players. In new signing Joao Cancelo, the Portuguese will ensure Kyle Walker has to work for his place before eventually replacing him.
Oleksandr Zinchenko was City’s break-out player from last term and has displayed enough skill to act as a back-up for the constantly injured Benjamin Mendy.
MIDFIELD – A+
The best midfield in Europe surely deserves top marks.
City have Rodri, Kevin De Bruyne and Bernardo Silva as their first choice midfield three. A dream trio. The former enjoyed a stunning season at Atletico Madrid and is tipped to shine in Guardiola’s system. The latter two were among the best players in City’s title-winning season and are showing no signs of slowing down.
Their back-up midfield of Fernandinho, David Silva and Ilkay Gundogan are capable of starting for most teams around Europe. This depth will allow them to compete for the Champions League and sustain their domestic dominance at the same time.
Their seventh midfielder Phil Foden, 20, is one of the best prospects in the world and is likely to climb higher in the hierarchy over time.
City are set to dominate the Premier League again and there is little scope for improvement in this flawless midfield.
ATTACK – B+
There’s a thin line between midfield and attack in Guardiola’s system. This was evident last season when Bernardo was deployed as a right-winger regularly. Foden was also called in to take guard in the left-wing in some games when he came off the bench.
Regardless, the wings are well-equipped with fire-power that accompanies the likes of Raheem Sterling, Riyad Mahrez and Leroy Sane. The latter is set to miss the first half of the season due to a torn ACL but Sterling’s versatility should ensure City don’t miss the German that much. The option to step midfielders higher up the pitch is also present, as is the option to deploy second choice striker Gabriel Jesus on the left.
Sergio Aguero will spearhead the attack again in search of yet another goal-laden campaign. The versatility of the players in midfield and attack should more than make up for any injury-related complications that could arise during the season.