The result marked back-to-back wins for Silva's side, who sit eighth in the table ahead of a tough home encounter with Manchester United on Tuesday evening.
"We won the game, really important for us, we got a fantastic result," Silva told BBC Sport after the final whistle. "Congratulations for our players and our fans, their support was really good for our team but congratulations to the fans of Newcastle, fantastic today and always support their team.
"We deserved the three points. We had very good moments, we scored the first goal through something we planned. The confidence in some moments was good, we knew they were strong in the long balls and first and second balls and I think we controlled really well.
"It is important for our players to play with this confidence. It is important for them to rest now and we have a hard game against Manchester United on Tuesday."
Watford will go into the game with the chance to cut the gap on high-flying United to just five points.