David Nugent netted eight minutes from time to give the Foxes a 1-0 lead to protect in Sunday lunchtime's second leg at Vicarage Road. Both sides had created chances prior to Nugent's header. Leicester's best openings came during the first half while Watford's Ikechi Anya and Matej Vydra spurned one-on-one opportunities either side of the break.
"I think we were punished for not being clinical enough," said Hornets boss Zola, whose team were easily the highest away scorers in the division during the regular season with 44 goals.
"In other games we have created less chances and still won. I couldn't see Leicester scoring, I thought we had control of the game. But this is the reality and the Championship is like this, teams can punish you with very little opportunities. When you have good players like they have, this happens.
"It is a shame because scoring and taking chances has been one of our main qualities. But it is okay. I can't be too hard on my players because they played a good game and they deserved more. I don't think anyone can say we deserved to lose. It is hard on us, I think a draw was probably fair. Leicester also had chances in the first half but they were matched by our ones."
Zola remains confident of turning the tie around at Vicarage Road in three days' time. He added: "Now we need to get ready and play the best game of our season as that is what will be necessary to beat Leicester. But I am sure we can do it. I am confident because we have goals in our side and we will have Troy Deeney back from suspension."
Nugent headed home Anthony Knockaert's free-kick in the 82nd minute to end a 16-game goal drought. Foxes boss Nigel Pearson was pleased to see the striker break his duck but insists the recent lack of goals has not affected the player or the team.
"Strikers thrive on goals and hopefully it will give him that extra confidence,'' said Pearson. "Not that he's been lacking confidence, really. He always gives you enthusiasm and work rate and affects the game.
"Normally when he gets one goal he gets a few. It has been a while but with him around he's always capable of scoring. I'm pleased for him but more importantly he's got us a narrow lead.''
Asked about the second leg, Pearson added: "It's evenly poised and both sides will feel they have good chance of progressing. It's going to be tight, as both sides will have expected. It's nice to go into the second game with a narrow advantage but we will try to win that one as well because we are a better team when we are on the front foot."