Micah Richards said the Manchester derby was a "bad day for referees" after City claimed a 1-0 win with a controversial goal.
The game was clouded by two contentious decisions, which first saw Phil Foden sent off for City for reacting to a Bruno Fernandes kick.
Ten-man City then took the lead on the hour through Erling Haaland, who initially had the goal ruled out for offside before the decision was overturned by VAR.
Speaking on Sky Sports, Richards said: "I think it's been a bad day for referees, I think it's been a bad day for VAR.
"I think they got the Phil Foden decision wrong after 23 minutes and they got this decision wrong. How you can say Enzo Fernández is not challenging ... Of course he is.
"I've been in that position as a defender where any slight movement can make the difference between going for the ball or not. Of course it affects him.
"I just think they got it so wrong, but that doesn't take anything away from City's performance. To go that long with 10 men is just incredible.
"We talked about fight, we talked about spirit, new manager, first derby, what have you got? They showed exactly what they are."
A post on the Premier League Match Centre X account explained the reasoning behind the decision.
The post said: "VAR checked the referee's call of no goal for offside - and determined that Haaland was in an onside position and recommended that the goal was awarded.
"The VAR also deemed that while in an offside position, Fernandez didn't play the ball."
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Offside rules relating to interfering with a opponent state that a player will be penalised if they are:
"Preventing an opponent from playing or being able to play the ball by clearly obstructing the opponent's line of vision; or
"Challenging an opponent for the ball; or Clearly attempting to play a ball which is close when this action impacts on an opponent; or
"Making an obvious action which clearly impacts on the ability of an opponent to play the ball."
Sky Sports pundit Roy Keane believes City were "more streetwise" than United to snatch the win.
"City were smarter than United. United when City went down to 10 men, United players maybe started overthinking it," he added.
"Again, keep it simple, still do the simple things right. City were certainly more streetwise."
