Ryan Sessegnon struck the winner in today's early kickoff.
Silva said afterwards: "Overall good performance from us. We would've liked to have a bit more of the ball in the second half, to have longer periods of possession and be able to create more.
"We pressed them very well every moment. A top side with physical and technical players but we needed (to win) and we wanted it.
"We created good moments. Second half it was difficult to press, we needed a bit of calmness and quality and could've created more. Back-to-back clean sheets in a crucial moment."
The win moves Fulham within two points of sixth place.
He added: "Massive win against a top side. Always capable of finding moments to score the way they build through the spine of the team.
"Our work was good. Two points off sixth and it's going to be a big fight until the end. We have set ourselves in a position to fight for something so that should make everybody proud. It will be difficult. We have lots of injuries but we keep fighting to make people proud of us."