The loss at the Allianz Arena was the biggest in the competition's history at the last-four stage and represented the Blaugrana's heaviest away defeat in European competition. The club's chief playmaker admitted afterwards that the Catalans could have no complaints about the final scoreline.
"It's the worst result ever," Xavi told reporters. "They were better - and I don't mind saying that."
The Spain international also conceded that the Liga leaders have little hope of turning the tie around in the second leg at Camp Nou next week.
"It's almost impossible," Xavi said. "But we must try to, for this club and for everyone."
Barcelona made history in the quarterfinals by recovering from a 2-0 loss away to AC Milan with a 4-0 victory in the return leg to progress 4-2 on aggregate after a stirring comeback.