The influential midfielder feels the Camp Nou side deserved more from the Copa del Rey final and has urged his team-mates to bounce back in La Liga at the weekend
Angel Di Maria gifted Madrid an early lead at Mestalla before Marc Bartra restored parity in the second half, but Gareth Bale eventually helped the Santiago Bernabeu side to cup glory with a superb solo goal in the closing stages of the game.
"They took advantage of their weapons. They hurt us with their counterattacks," Xavi was quoted as saying on Barcelona's official website.
"We would have liked to win this for the fans. We should have won but we didn't. If anyone is at fault, it's the team. From the manager to the players. These are our errors, and our rival took advantage of them.
"We still have La Liga, and it will be difficult to win it, but we will continue fighting for the title. We have another war on Sunday. We lacked effectiveness because we missed cleared chances."
Barcelona resume La Liga action at home against Athletic Bilbao on Sunday.