The Hornets missed the chance to climb up to second in the npower Championship after Burnley sub Sam Vokes pounced on a slip by Matthew Briggs at the back to secure a 3-3 draw in stoppage time.
"I thought we'd done enough," admitted Hornets boss Zola. "We came back from behind twice and then went ahead, and towards the end I didn't see that coming, but it's not the first time that has happened.
"A sloppy piece of defending costs us a lot. I understand we have a very young team, but there's not much time for them to learn, we need to grow up quickly.
"We have done very well so far and it would be a shame not to finish what we have done. It was a pity because Briggs played a good game. Today it was him but other times it has been someone else.
"Now is the time we cannot give anything away, every single game is going to be very difficult."
Watford could have leapfrogged Hull into second with a victory, but instead the Tigers will be four points clear by the time the teams meet on Tuesday if they beat Huddersfield on Saturday.
Burnley manager Sean Dyche, who was axed by Watford's new owners and replaced by Zola in the summer, insisted he took no extra satisfaction from the result.
"No, not because it's at this club," he said. "But I do take great satisfaction in the manner we performed and in the way we got a point after a ding-dong Championship clash.
"I thought the game fluctuated around mistakes to be honest. Charlie is a player with goals in him, and I thought he could have had a couple more. But I'm not frustrated. Watford are a very good side. They've got every chance."