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Goals from Anthony Martial and Scott McTominay at Old Trafford saw City lose to United for the second time this season.
Although Pep Guardiola's team saw a lot of the ball - finishing the match with 73 per cent possession - City managed just four shots on target in the 90 minutes against their rivals.
The defeat was City's seventh in the Premier League this season and leaves the reigning champions 25 points behind leaders Liverpool in the table, meaning Jurgen Klopp's team can claim the title by the end of March.
Guardiola defended his side's display despite the defeat, saying that his side played well and were only lacking in the final third of the field.
But Portugal winger Silva had a different opinion, as he admitted his side were not up to the standard expected of them this weekend and urged them to bounce back in their next game.
"It was a bad game for us. Not acceptable. We didn't start badly and were playing quite well until we conceded," he said to Sky Sports after the match.
"We know how good the Manchester United players are on the counterattack, very aggressive. So our performance was not acceptable.
"We will have to watch the game back and listen to what Pep has to say. But a team like ours cannot lose this many games. We need to check what's not going right and try not to make so many mistakes."
He continued to BBC Sport: A very bad day for us, it is always a special game even though we are not going for the title. It is a special game for our fans and us and we need to do better. It is not acceptable to play this way and lose like this.
"We started well but everything changed after the goal, a very bad performance in my opinion.
"Possession is important in a way but does not dictate if you play well or not. We did not control the game as we should have and maybe from the perspective of people watching the game, we had more possession but they had the more clear chances. A bad performance.
"I don't think it will affect performances in the Champions League. It is not acceptable to come here and lose 2-0."
City are in action again on Wednesday when they host Arsenal, pitting Guardiola against his former assistant Mikel Arteta, who took charge of the Gunners last December.
Three days later, City will take on Burnley at home in the English top-flight before they turn their attention to the Champions League last-16 clash with Real Madrid, having won the first-leg in the Spanish capital 2-1.