The Cottagers overcame Saints' lead through Jack Stephens to win 2-1 with two late goals through Emile Smith Rowe and Ryan Sessegnon.
“I agree, well deserved," declared Silva. "If someone has to win this game, should be Fulham Football Club.
“I know that we conceded an early goal from a wide free-kick where we should have done much, much better, but the reality is that from the first minute until last, we are the only team that tried to score goals, tried to play in an offensive way.
“I know that they scored early, but after that they just tried to not let us break them down.
“They sat around their box, 9/10 players around the box. And all that time it is not easy to break this type of teams down because they just wanted to keep the result and not really to chase the game.
“These are the moments that you have to show patience, but at the same time put the right moves, the right timing, even if our first half was completely below the standards and the quality that we have to play at this level, even so I think we did create enough."
"Only one team wanted to score"
In the aftermath, Silva took aim at Southampton's defensive tactics and was pleased to see Fulham's pressure eventually see them breakthrough.
He said, “We have lacked some confidence, trust and quality in the 18 yard box. We need to create much more, with the last pass, the last finish. But even so, I think we did create enough first half to have a different result at half-time.
“And second half was the same story again – one team trying to create chances to score, playing 90 per cent of the time in our offensive half. They sat back, they just tried to delay our goal or chances that we can create.
“And I think we did create enough – (post) from Willian, some good moments from the left, from the right.
“Of course, we added some different characteristics from our players at half-time, with Adama and Lukić a little bit more dynamic in that position, to set up Harry Wilson more in the pocket, more inside, almost as a second striker.
“And we started to create more – crosses from the left, from the right, inside as well. I think we did create enough. The goals came late, but overall clearly one team deserved to win, and that is ourselves.”