Saints were restricted to just one shot on target in the whole game, which came in injury time, and Silva was happy with how his side dominated proceedings on the south coast.
The Portuguese coach told BBC Sport: "It is really pleasing, and I am really proud of what we did.
"Congratulations for our team and our fans, they created a fantastic atmosphere and we deserved the win. It is not easy to come here and play how we played and control it how we did. We put pressure on the opponent, I do not remember a clear chance for them.
"The players work every day and this commitment and attitude means we can enjoy the match. Three clean sheets in a row is very important and gives the team confidence, but we played at times with a lot of quality and deserved the three points as we were stronger than our opponents.
"If you analyse the matches, we have had a lot of problems, we have used six centre-backs and that is not normal, but we have kept three clean sheets. It is a very good start but we need to continue in this way."
The result saw Watford remain one of only four top-flight sides yet to lose in the league this season and edged them up to fourth in the table.