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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