Ole Gunnar Solskjaer's side welcomed their bitter rivals to Old Trafford on the back of two positive results against Tottenham and Atalanta.
But they were powerless as City came away with all three points.
Goals from Eric Bailly (own-goal) and Bernardo Silva gave the away side a 2-0 victory.
The scoreline doesn't paint the whole picture, though.
City were by far the superior side and could easily have won by a bigger margin.
David de Gea's display was one reason why City only won by two goals.
Midway through the first half, the Spanish stopper made five saves in just seven minutes.
It was a very poor day for United but De Gea is maybe the only United player that could hold his head up high.
The 30-year-old is doing everything he can at the moment and he showed how much he cares at half-time.
De Gea was visibly fuming when making his way off the pitch.
Fan footage has emerged of him punching the tunnel in anger as he made his way to the dressing room.
Fair to say De Gea was a little upset during his side's defeat.
Fans have been reacting to the footage and many are sympathising with De Gea. View some of the comments below...
United remain in fifth in the Premier League having accumulated 17 points from their opening 11 games.
SACK SOLSKJAER NOW! Manchester United 0-2 Man City Match Reaction
They are now six points behind Man City and a further three points behind league leaders, Chelsea.