The Cottagers won 3-0 thanks to goals from Harry Wilsson, Rodrigo Muniz and Adama Traore.
Silva said, "Really pleased and a great team performance. We were brave and knew when to press. We had a good mix and executed our game-plan really well. We were more assertive in the first half rather than the second.
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"The spine of the team did really well this afternoon and we knew it would be important to win that battle.
"It's really difficult to have back-to-back wins in the league, we haven't had many this season.
"It's very important and gives a good feeling. After the last home game against Aston Villa it was important to react and we did that against Manchester United and then another good win today.
"We want as many points as we can to climb up the table."