Matej Vydra fired the Hornets ahead in the 15th minute before Forest were reduced to ten when Daniel Ayala picked up a second booking and Vydra then added a second in the 40th minute.
Zola admitted his side took their foot off the pedal after the break, but was still satisfied as the win lifted Watford back into the top six.
"The first half was excellent. Some of the things that we saw were really good," said Zola.
"I cannot say the same for the first 20 minutes of the second half, in which we took the foot from the pedal completely and we allowed them to come back into the game a little bit more.
"That wasn't necessary but I can understand. The team felt like the game was gone so that is something we need to address. But at the end of the day it's good. It's three points to go into Christmas."
Asked what pleased him most about the win, Zola replied: "I think it was a tricky game because Nottingham Forest is a good team and so you didn't know what was around the corner for us.
"Also, we're coming from two games in which we didn't play our best football; against Hull City and Burnley we didn't play to our normal standards.
"It was 50-50 but fortunately the way we started and, above all, the form of the two strikers made a big difference today."