Jamie Ward had scored twice either side of a Fernando Forestieri goal to give the Rams a 2-1 lead at the break before Lewis McGugan equalised to bring Watford level for a second time midway through the second half.
Conor Sammon came on to snatch the winner for Derby late on.
"It is tough to take but I have to say we have to blame ourselves," the Italian said. "It is not enough to play good football like we did here, it is not enough to score two great goals like we did. We need to get better in defending.
"To win championships you have to be able to attack well as we did here and as we can do but we need to defend better.
"We want to do better than we did last year and to do that we need everyone to improve, so we need to defend a little bit better than that. And when I say that, that doesn't mean it's only the defenders - everyone does.
"The midfielders and the strikers have to work a little bit more because in modern football you cannot think you only defend with the defenders. Everyone has to participate."
Two of Derby's goals came from Watford giving away possession, and Zola added: "When we analysed the opposition we said this team is very dangerous.
"Before this game they won four games, three of them were away from home. We saw them and they were very dangerous when you lose the ball and they start counters and I think some of our passing on the deck was very poor - or at least not as good as normal and that's something we cannot afford."