Alvaro Garcia scored a 7 minutes beauty to hand the blaugranas a second home loss and achieved the double over the Catalans.
The loss means Barcelona have all but given the title to madrid after a 14 games unbeaten run had given them a slim hope.
The coach has taken all responsibility and criticism as barcelona pushed hard for an equaliser that never came.
Mistakes cannot be repeated,” Xavi told his post-match press conference. “We must be self-critical. It’s our reality. We have to match the desire, the desire of our rival.
“We were excited about a good run, with the good games in the Europa League. Now, it is not very motivating to fight for second place for a club like Barca, but we have to improve.
“We have to go into the games better. In the first half, we were not good. In the second better. We tried everything but the situation is difficult.
“I recognise as a coach that I made a mistake in not motivating them.”
Despite the recent slump in form, Xavi had revolutionise a turnaround and he went on to say
“We have lost two games at home that we had to win against Cadiz and Rayo,” he added. “But we arrived in November when the team were ninth, with emergencies in the club.
“These are games that are complicated, but it is football. We have to think about Mallorca, disconnect [from this result] and prepare for this game. There are five finals left.”