The Sky Blues were up 3-0 at the interval, with a Marcus Rashford strike seeing the game end 3-1.
But Silva is adamant City were capable of extending their lead before the half-time whistle.
"I think we could have gone to half-time winning by four or five because we missed a few chances, then the second half was very hard for us," Silva told Sky Sports.
"They started pressing higher, trying to control the game and getting on the ball. We got a bit tired, but I think overall it was a good performance and we're happy with this win.
"It's never easy to come here to Old Trafford against one of the best sides in England, in Europe, and to win 3-1.
"When you play a derby and you play Man United, you cannot always win. We were disappointed because losing at home [to United in December] is not normal for us. Coming here, in a way it makes it up to our fans, who once again were unbelievable in helping us get this win."