The Spanish champions were thrashed in Saudi Arabia by their bitter El Clasico rivals and Xavi said his team gave a bad account of themselves.
"We were lacking in every way and have to apologise to the fans, we did not show the level to compete in a final," Xavi told reporters.
"It's a heavy defeat, as a Barca fan I'm disappointed, we put on one of our worst displays of the season.
"This is not the image that Barça have to show, especially in a final against Real Madrid."
Vinicius Junior hit a first-half hat-trick for Real Madrid, including a brace inside the first 10 minutes, with Robert Lewandowski netting for the Catalans.
Rodrygo rounded off Real Madrid's rout in the second half, while Barca defender Ronald Araujo was sent off for two bookings, both for fouls on Vinicius.
"We did not stop counter-attacks and runs, we started in the worst way in a final, we were trailing for the whole game," added Xavi.
"We reacted well with Robert's goal and then with the penalty, the game basically ended there."
Xavi said his team had to work on their mistakes after the defeat, but that three trophies were still at stake this season.
Barcelona visit third-tier Unionistas de Salamanca in the Copa del Rey last 16 on Thursday.
"It's a trophy lost, we have to be self-critical (but) I still believe in the project and we can still have a great season," said the coach.
"I think we can turn the situation around... everything continues, I've been in these situations many times, there's nothing for it but sucking up the criticism."
