The Cottagers lost a 34-strike shootout after Reiss Nelson had canceled out Ryan Ledson's opener for Preston. It was Ledson who struck the winning penalty for Preston.
Silva said afterwards: "I think, no I'm sure, that we did enough during the 95 minutes to win the game.
"From the first minute, we took control of the game and I think we created enough chances to score more goals. That is the situation.
"We created two or three chances that we should have scored. One rebound in that moment on the edge of the box and they scored. A very good reaction from us second-half. We took control of the game all second-half. A good goal from us.
"Some good chances again, the crossbar, a lot of crosses, a lot of moments where we should have scored. We didn't and after in the penalties, they scored one more than us, one goal, and they are in the next round."
On Nelson's first goal for the club, Silva continued: "Very good run from Sess. I think he's improving, he's getting better. From the first minute until the last minute, he kept composure always. He was strong defensively and, of course, offensively we know that he is capable to do.
"It's important for him to get the confidence he needs because all of us know the quality that he has."
Sander Berge also was given his first 90 minutes since joining Fulham.
"It's important for him to get 90 minutes for the first time with our shirt and he's going to be, step by step, in the condition that we need him to be to play the Premier League games," added Silva.