Raul Jimenez struck twice, with Alex Iwobi also scoring for the visitors. Sunderland's goal came from Enzo Le Fee.
"A big win,” Silva said. “We knew that it was going to be another crucial game for us - very important.
"We came into it with some not good results for us in the Premier League, of course, after an incredible run during December and January. We wanted to bounce back at a place that has been very difficult for other teams to play, against Sunderland.
"It's a tough place to come with incredible support, they are capable of pushing them forward and making life difficult for the opposition. It's been working well for them and we knew it.
“Of course, the pitch wasn't perfect for both sides. We knew that this game needed certain types of characteristics and we did it. We knew that we had to keep the organisation and the composure, and we had to be aggressive."
Silva added, “Credit to Sunderland for the way they made life difficult for us, as always. But overall I think we deserved the three points. It's a big win for us.”