Manchester City boss Manuel Pellegrini was bitterly disappointed after seeing his side suffer their second defeat in seven days.
Strong contenders to win the title last month, the Citizens lost five of their last seven games in all competitions as they continue to fall short against the big teams in the domestic league.
They will try to take advantage of their next two home games against West Ham United and Aston Villa to improve their disappointing position in the table.
"I think they were the best team," Pellegrini said.
"We started very well and in the first 20 minutes we could have controlled the game. After the second goal we lost the way we were playing and United scored more goals.
"I don't understand why a team only plays so well in the first 20 minutes. We dominated, created chances, we had the ball.
"At 1-1 United started growing and their third goal gave them the confidence they did not have before.
"It is not just one problem, the same team played well for 20 minutes. Maybe it's a lack of class at this moment. I don't know."