The Hornets twice led proceedings at Vicarage Road but found themselves 3-2 down for the final half-hour of the contest after a Roberto Firmino penalty and a goal from debutant Mohamed Salah put the Reds in the driving seat.
"Of course I think it is a good result for us and a fair result," Silva told Sky Sports News. "It was a very good first half for our team, good rhythm. I didn't like the first 25 minutes of the second half.
"We expected a good reaction from our opponents but to play with the same intensity.
"We reacted well and left it until the end, it is really important to us and we really, really deserved the result as well."
Next up for Silva's charges is a trip to the south coast to take on Bournemouth next Saturday.