City, the champions and league leaders, opened up a 12-point lead over their neighbours with a deserved 3-1 derby win at the Etihad Stadium.
It was United's fourth defeat in 12 games and left them eighth in the table.
City manager Pep Guardiola had said before the game that United could not be written off as challengers even if they lost, but Silva thinks they could have their work cut out.
The Portugal international said: "It won't be easy. Not only Man City - (they are) 10 points from Liverpool, a lot of points from the other ones as well.
"They need to be almost perfect and wait for the other ones to lose a lot of points. I think it won't be easy."
The derby saw City show their clear superiority over United but it was not until the latter stages the points were made safe.
City powered into a 12th-minute through David Silva but United then tightened up and it was not until the 48th minute that Sergio Aguero doubled their lead.
An Anthony Martial penalty just before the hour gave United hope of repeating last season's stunning comeback victory over City at the same venue, but this time the hosts proved too tough to break.
City reasserted themselves and made victory certain as Ilkay Gundogan finished off a 44-pass move with a third goal four minutes from time.
Silva added: "After their goal we knew they would have confidence to try to come for a second but I think our performance was amazing. We didn't concede one chance - only the penalty.
"I think the team was very concentrated, very focused on what we had to do. Everyone has to be congratulated for their job. Three more points - top of the league, on to the next one."
City have dropped just four points this season and have scored 36 goals from 12 games, conceding just five. At this stage last year, however, they already had an eight-point lead at the summit. This time they are just two clear of Liverpool.
"We know it won't be easy this season," Silva said. "Liverpool are doing a fantastic Premier League as well.
"We want to try to and have a bigger gap during the months of December and January, where you have a lot of games. We will work very hard for that and try to improve on this."