Riyad Mahrez headed home the opening goal of the game after 37 minutes, before Mali international Molla Wague equalised for the Hornets on the stroke of half-time.
The Hertfordshire club were buoyed by Wague's goal and their momentum culminated in Foxes keeper Kasper Schmiechel diverting Abdoulaye Doucoure's volley into his own net with 25 minutes left to play.
Speaking after the game, Silva believed his side had done enough to deserve the win.
"We controlled the match," Silva told Sky Sports. "One moment they score, and recently, it has not gone for us when we go behind. Last performance it did not go well.
"We played against a balanced team, who have good players in attack. We knew before the game that they are very good on the counter attack. If they catch another team unbalanced, they are strong.
"Today, we showed very good personality, a big mentality to react like we did after it went 1-0. The last minute of the first half, we score, then we could have scored again through Richarlison.
"This is our normal mentality. Of course the last few results have made our players a little uncomfortable, but we were good this afternoon.
"I think we deserved it because we showed this good personality.
"The commitment was great to see. All the games are very important for us. Now it is important to rest, we then play again at home, and we need the support of the fans here all the time, through good times and bad."