Fulham went behind to Cauley Woodrow for Wycombe before leveling through Josh King to take the tie to penalties.
Defender Issa Diop scored the decisive spot-kick in sudden death to give his side a 5-4 shootout win after goalkeeper Benjamin Lecomte saved three Wycombe penalties.
Afterwards, Silva said: “We wanted to be in the next round. We are going to be there. Of course, our obligation was to be in the next round.
“To be honest, I think throughout the game we did enough. We knew we had to be positive and keep positivity around ourselves because these types of things happen, where the first shot on target was a goal. That’s football, and I told the players at half-time that sometimes things come against us and we have to face it in the best way we can.”
Silva also admitted: “The first half was not at a good level but we did create some chances – not clear cut chances – and we didn’t suffocate them like we should.
“Second half, we pushed them back and created six or seven clear chances to score. That’s football – when you create like we created in the second half, we have to put the ball in the back of the net. We have to be clinical, we have to be ruthless.
"We are in the next round and that was the most important thing for us. In that away end full of our fans, I have to thank them for the support. We understand that they were unhappy at half-time with our performance.”