The Hornets failed to take advantage of Hull's draw with Cardiff on a final day of high drama, instead suffering a late defeat to Leeds that consigned them to the play-offs.
But Zola insists spirits in the squad remain high ahead of Thursday's first leg against a Leicester side who, by contrast, snatched a shot at the Premier League thanks to an injury-time winner against Nottingham Forest.
"The last couple of days have been very good," Zola said. "Obviously the day after the match we all felt it, we knew we had lost a big opportunity but that is part of football.
"We had a wonderful evening on Sunday when we had the end-of-season dinner with the supporters and it was great. After that everyone felt a lot better and it's been getting better and better since then.
"The disappointment of Saturday is over and we are ready to compete again. There is a determination to compete against a good team and to achieve something we think we deserve."
Watford ran out narrow 2-1 winners in both their meetings with Leicester this season and Zola expects two more tight matches, with the second leg at Vicarage Road on Sunday.
"I believe it will be even closer but we are in a good moment, we know we have a good team and we have been playing well recently," he added.
"When we started the season we did not expect to be third, we wanted to build for next year so we are happy to be third and there is not any pressure."