Brennan Johnson had Spurs ahead before Tom Cairney struck - and then was later sent off.
Silva said, "I think that everybody should recognise that the team who deserved to win this afternoon was ourselves. We deserved to win. We played our way with our identity on the pitch. Myself, the players and the fans should be proud of it. We should have been leading the score with the chances we had, we have to be realistic Tottenham had chances as well."
On Cairney's red card, he continued: "Firstly I know him, Tom Cairney is not the player for that, everybody knows. I have to be realistic and honest with you, everybody knows I am the first one asking him to be more aggressive in the right way, to keep some principles as a midfielder in that situation but he is not the type of player to do that type of thing.
"He stamped on his leg and of course looking for the images it should be a red card and we have to accept knowing Tom Cairney was really unlucky because he is not that type of player."
On the reaction to going down to 10 men, Silva added: "What a reaction from us. The reaction was good, 15 minutes with 10 men and the reality is that Tottenham didn't create one chance."