Manchester United suffered a 2-0 defeat to Manchester City at Old Trafford as Pep Guardiola’s side returned to the top of the Premier League table.
Solskjaer’s side started the match strongly with the Norwegian’s men clearly looking to make amends for their 4-0 defeat to Everton last time out.
But the Red Devils came unstuck in the second half as City found another gear.
City came out firing in the second half and took the lead in the 53rd minute.
Bernardo Silva ran at Luke Shaw and unleashed a low shot which beat De Gea at the near post.
And moments later the game was put to bed with De Gea again failing to keep the ball out.
The visitors hit United on the counter-attack and after Raheem Sterling fed Leroy Sane, the 23-year-old drilled a shot that the Spaniard failed to stop despite being straight at him.
While TV cameras caught Guardiola celebrating wildly on the touchline, in the opposite dugout Solskjaer lowered his head to his chest at the error.
A thrilling encounter at Old Trafford also saw:
United have now suffered seven defeats in their last nine matches and remain three points adrift of fourth placed Arsenal – who suffered a 3-1 loss to Wolves on Wednesday evening.
Meanwhile City, who have won their last 11 league matches, now lead Liverpool by a point with three games remaining for both sides.
The match had long been identified as a tricky hurdle for City but with games against Burnley, Leicester and Brighton in their run-in, they will now be regarded as clear title favourites.
It was a victory Pep Guardiola’s side certainly had to work for and show all their champion qualities to achieve.
Suggestions United might prove pushovers after a dismal run of six defeats in their eight previous games, or they would be unwilling to do rivals Liverpool a favour, were wide of the mark.
Solskjaer refused to place the blame at De Gea’s door at full-time but admitted his team have a long way to go to get to City’s level.
“We got a reaction and in the end we were beaten by a better team. But we got a reaction from fans and players and had a go. You can see the work-rate was there, it wasn’t good enough,” he said.
“There is a difference in quality. That is why they are top and we are where we are. They have set the standard. Living in Manchester we cannot be happy with that. It is up to us to close that gap and overtake them.
“Today you can’t say that any of them didn’t run. You could see clearly an intent and focus. We just need to keep working on it.
“City want to win it back and by their aggression to win it back there will be fouls. They keep the ball high and are hungry to win it back. They stopped us very well.
“David [De Gea] made some terrific saves as well today. It is every day work for everyone. He has high standards. When we are having a time like this we need to stick together, batten the hatches down and keep working. We have to come back fighting on Sunday.”