Saturday's 2-1 home loss to Quique Sanchez Flores's side in the quarter-finals ended Arsenal's two-year hold on the competition and they will now focus on attempting to overturn a 2-0 deficit when they visit Camp Nou for Wednesday'sChampions League last 16 second-leg match.
The odds suggest Arsenal will return from Barcelona having exited another competition, adding to the pressure building ahead of this weekend's Premier League visit to Everton, when they will attempt to maintain their slender title hopes.
The loss to Watford has done nothing to strengthen belief and Wenger said: "It's always difficult after a defeat, but it is our job to prepare for the next game.
"Our long run in the FA Cup has come to an end in a very sad way because I don't think we deserve to lose this game."
He added: "We have shown we can respond always. I think this team has a great spirit, a very strong attitude.
"They play at the moment with the idea we cannot afford any result, you know. We have an opportunity to show on Wednesday night we are up to it.
"We won't rest players. We want to make the impossible possible and we know we play against a very strong, strong side and it's important we go there and focus and show a very good response."
Second-half goals from Odion Ighalo and Adlene Guedioura set Watford on course for the semi-finals and Danny Welbeck's 88th-minute reply came too late to spark an Arsenal comeback.
Amazing for Watford
It could have been worse for the home side had referee Andre Marriner taken a different view of Gabriel's studs-up challenge on Watford captain Troy Deeney, for which the Brazilian escaped without a caution.
"I have to see it again," Wenger said. "He won the ball. I think Deeney as well (had his feet off the ground).
"They both went for the same ball and Gabriel was first to the ball. That's how it looked. Maybe if his feet were off the ground, maybe I will have to look at it again."
Watford manager Flores hailed the success as one of the high spots of a career that includes a Europa League success with Atletico Madrid.
"We have confirmed we will play in the semi-finals in Wembley and it's amazing for the people of Watford, the fans, the club, the players," he said.
"It's an impetus for the last part of the season. I have memories on television of the old Wembley and watching in Spain and seeing the finals of this competition.
"Now it is a new Wembley. I've just arrived in England, and to get there is exciting. I'm really happy for the fans and they deserve this kind of day."
He added: "This is the most important game of my career. We are Watford, and we will try to enjoy this journey, this experience.
"This season has been amazing for Watford. Maybe we have the temptation to think in the past month that Watford is going a little bit down, but that's normal."