The Premier League leaders secured a 14th win in a row – a record for a single season in the English top flight – and an 11-point lead at the Premier League summit thanks to goals from David Silva and Nicolas Otamendi either side of a Marcus Rashford strike.
City dominated possession at Old Trafford and looked unlikely to allow United back into the game for a second time after Otamendi's winner, although there was a controversial incident with 11 minutes left when Ander Herrera was booked for diving after being clipped by the Argentine defender in the penalty area.
Mourinho believes that decision from referee Michael Oliver cost his side the match and pointed to a similar incident last season, when Claudio Bravo escaped punishment for a lunge on Wayne Rooney as City saw out a 2-1 victory.
The United boss told Sky Sports: "Clear penalty. I'm sorry for us, for Michael, I think he had a good game but it's a clear penalty. Don't you agree?
"The referee made a mistake, which can happen. Last season, we had a similar situation against Manchester City, who were winning 2-1 and Mr [Mark] Clattenburg didn't see the penalty of Bravo on Rooney.
"I'm sorry for Michael Oliver because he had a good performance.
"He is a human being, he tried his best, he was very committed to have a good match, which I think he had. But he made one mistake and it was the crucial mistake for the result of the match."
United had eight shots to City's 14 and managed just 35 per cent of the possession, but Mourinho was left angry at the way his side conceded twice after failing to clear their lines from set-pieces.
He did, however, credit the visitors for their approach as they ended United's 40-match unbeaten run at home, which stretched all the way back to the derby defeat last September.
Mourinho said: "They scored two very bad goals. They scored two goals that are quite unbelievable to concede and when you concede two goals like this, in a match of this dimension, you obviously feel bad because now you're all going to speak about what they do well, what they're good at, and in the end what they're good at, they were not good at, and they scored two goals out of nothing.
"We did good things, we did bad things. We have a complete dedication to the match, every player trying to do their best. We know they're very good in ball possession, very good at bringing their full-backs inside and they also had an extra man with the striker dropping back.
"Even if you try to press, it's really difficult to recover the ball, so credit to them for that quality they have in their principles of play."