United have now lost seven of their last nine games in all competitions, leaving them three points outside the top four in the Premier League.
But they have been helped by the stumbles of others, with Arsenal’s defeat to Wolves on Wednesday night keeping the door open.
Chelsea, who sit in fourth, visit Old Trafford on Sunday and Solskjaer has urged his side to keep fighting for Champions League football.
“We need more quality on Sunday and if we win that game, we have two games to go,” Solskjaer said.
“Of course we want to get into the top four. I haven’t been planning on playing on Thursday nights yet. We just have to make sure we give ourselves a chance on Sunday.
“We’re three games away from the end of the season, we’re three points behind the top four and no-one would have given us a chance a few months ago.”
Like Arsenal and United, Chelsea have also endured some disappointing results of late, missing their own chance to pull clear when they drew at home with Burnley on Monday night.
Maurizio Sarri’s side could be feeling the pressure, and Solskjaer called on the Old Trafford crowd to turn up the heat further this weekend.
“Sunday is a massive one,” he told MUTV. “Sunday is something we have got to get ready for. The crowd has got to get ready for it, the players have got to get ready for it.
“Of course we have analysed them. Let’s just make sure we turn up on Sunday with the same attitude and a little bit more quality in front of goal hopefully.
“Let’s get the win that everybody wants, that the fans deserve and that the players deserve because they have made a terrific effort to give us a chance with three games to go to get in the top four.”
Tough period for us at the moment and as a United fan myself I understand how you’re feeling. We’ve shown how we can play, we need to get back to doing what we know we can do! @ManUtd— Marcus Rashford (@MarcusRashford) 25 April 2019
United’s poor recent form has been a particular disappointment given the football they played when Solskjaer first arrived as a caretaker following Jose Mourinho’s exit.
The Norwegian won 14 of his first 19 games in charge as United returned to exciting attacking play, but that has been in short supply of late.
They began brightly against City but could not maintain the intensity required, though they avoided a repeat of the insipid display of the weekend’s 4-0 loss at Everton.
Striker Marcus Rashford has been one of the brightest lights in recent weeks, and used Twitter to urge fans to keep the faith.
“Tough period for us at the moment and as a United fan myself I understand how you’re feeling,” he wrote.
“We’ve shown how we can play, we need to get back to doing what we know we can do!”
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Former Manchester United midfielder Roy Keane believes the club will struggle to recruit the players they need this summer because they are not challenging for trophies.
Keane, who was captain of United’s Treble-winning side in 1998/99 and lifted the Premier League trophy as skipper on three other occasions, was scathing in his assessment of the club while appearing as a pundit on Sky Sports for United’s 2-0 defeat by Manchester City on Wednesday.
In typically belligerent fashion, the Irish midfielder questioned whether the club’s hierarchy is up to the task of executing the rebuilt that manager Ole Gunnar Solskjaer insists is needed – and Keane’s former team-mate is not the first manager of the post-Sir Alex Ferguson era to say this.
“The worrying thing for me is that they need two centre-halves and two full-backs,” Keane said on Sky Sports. “That’s four for starters. And who’s making the final decision? You get the impression that there’s chaos in the background.
“I know Ed Woodward gets a lot of criticism, the scouting department – and will Ole [Gunnar Solskjaer] have the final say over [signing] players? I don’t know, because if you speak to the previous managers I’ll bet you that was a big problem for them.
“Also, which players out there, which brilliant players out there that are available will want to come to United? I always thought that when I was a player and up until the last two years, if I spoke to a player who had a chance to go to Man United I would say, ‘you’ve got to go.’
“I don’t care, brilliant club. Absolutely brilliant club. But you’re on about now players wanting to win the big prizes, then you look at Man United. If you’re a top player you will not want to come to Man United because there are better options out there in terms of winning trophies.”
Goals from Bernardo Silva and Leroy Sane in the second half secured all three points for Pep Guardiola’s men at Old Trafford.
Andreas Pereira was handed a rare start, his first since United’s Champions League clash against Paris Saint-Germain last month.
We take a look at how the 23-year-old performed in the derby.
Shots (on target): 2 (0)
Passes (success rate): 19 (79%)
If this was Pereira’s chance to shine and stake a claim for a place in the midfield next season, he didn’t do a lot of justice. The youngster ghosted in midfield and looked vulnerable to City’s press.
At times it looked like he was not on the same wavelength as Paul Pogba and Marcus Rashford and was hence dispossessed on several occasions.
Defensively, Pereira was average at best. In attack, he provided no threat whatsoever and was taken off after United conceded their second.
GOT RIGHT – Touches and defensive actions
The Brazilian had a couple of good touches in midfield and won the ball back in some crunch situations.
He also made a crucial interception on the right wing at a pass directed towards Raheem Sterling.
In the initial few moments when United looked to be the better team, Pereira was confidently halting City’s attacks and dispossessing them.
GOT WRONG – Press resistance
Press-resistance is a virtue and a player can’t be crucified for the lack thereof. But Periera’s show against City contained a different level of vulnerability to press.
The fact that he was dispossessed five times is evidence that Pereira really found it hard to play past City’s press. This attribute of his game prevented United’s counter attacks from taking off.
It’s fair to say that Pereira failed to make the most of the opportunity presented to him. He has not displayed anything close to the quality he showed while on loan at Valencia.
There are a lot of aspects the youngster needs to work on, with press-resistance and decision-making being the most important ones.
It would do him good if he improves his off-the-ball movements too, given how often he was positioned closer to the goal, leaving a void in midfield.
In Pereira’s defence, he was handed a rare start against one of the best midfields in the league and he was far from being United’s worst player. But he does need to step up his game when handed the chance to represent the club.