Victory over Leeds on the final day of the regular season would have earned the Hornets automatic promotion after Hull were held to a 2-2 draw by Cardiff.
But 10-man Watford slumped to a 2-1 defeat to Leeds at Vicarage Road, and they must now lift their spirits for the first leg at Leicester on Thursday.
Zola said: "It will be tough. They are a team we have already faced twice and we know the quality they have.
"They know us, we know them. We'll go there and play our game. Before the game the players knew the possible scenarios. We will be ready to start again on Monday.
"The players were very tired at the end of the match, they had given everything. It's been tough but we will come back.
"The expectations have grown this season as we have grown in stature but you have to face that if you want to be a top team.
"If you had said play-offs at the start of the season we would have taken it. Now we have a second chance to take our place in the Premier League."