The Hornets were in control by half-time courtesy of two composed finishes from Matej Vydra, both set up by excellent passes by Almen Abdi.
Forest's task was made even harder when Daniel Ayala, who was booked earlier, picked up his second yellow in the 38th minute.
Zola said: "The first half was excellent. Some of the things that we saw were really good.
"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."
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- Daniel Ayala