Anthony Martial gave the Red Devils the lead with a sumptuous finish half an hour into the game, before Manchester United academy product Scott McTominay delivered the hosts’ coup de grace to stun Pep Guardiola’s men.
Manchester United have secured their first Premier League double over the Citizens in a decade.
Speaking to the media after the game, Solskjaer admitted United are getting better, but insists his men must focus to secure a top four finish.
"With all the clean sheets we have been getting it's impressive, we are getting better,” the Norwegian said.
"With Brandon Williams and Aaron Wan-Bissaka on the flanks we looked aggressive as a 3-5-2, but in the second half we were made to look more like a 5-4-1.”
“City are so good on the ball, but we kept them at bay.”
"At any moment they could score so I was always looking for a second goal. We had three chances to square with only the goalkeeper to beat.”
“That's one thing to improve - our decision-making - but we are learning.”
"It's a privilege to be their manager. They give absolutely everything. They know they are all good players but they want to learn as well.”
"We feel we are improving as a squad and a team. We feel the fans want us to do well and they see what we are doing, so it is getting better and better.”
"But we are still fifth. We need points to catch Chelsea and Leicester, so need to keep plugging away."
Manchester United have now moved back to fifth place on the league table and are just three points behind fourth-placed Chelsea in the race for Champions League qualification.
