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."
Forest boss Sean O'Driscoll admitted he was trying to bring on Greg Halford for Ayala before he was sent off but "couldn't get him on quick enough".
He said: "I don't know what it was before half-time, not long, but suck it and see.
"That would have been preferable rather than getting him geared up but you think when you're on a yellow card and the referee's warned you that one more misdemeanour and you're off, you would be a little bit more cautious but Daniel's 20 years of age.
"We've all been young once and made mistakes and unfortunately he's made his."
- Sports & Recreation
- Daniel Ayala