The Rams went into the break 2-1 ahead but were pegged back to 2-2. However, substitute Conor Sammon's late goal proved decisive.
"I think we deserved the win. Watford are a good team, and it was a great game, end to end," he told Sky Sports News.
"We had good and poor spells but our character saw us through. I said before the game it's about the squad, not just the 11 who start. It was a good squad effort."
Derby's win moves them up to eighth in the Championship.