Bayern scored twice in four minutes against the run of play to move top of Group C, three points above second-placed Barca.
Barcelona had more possession than Bayern and outshot the German side 18-13.
"I am angry. I do not like to lose. We have not deserved it," Xavi told reporters.
"Last year I was angry because they were far superior to us. Today I think we played better than Bayern ... We dominated them, we subdued them.
"We created many clear chances to score and it would have changed the match. In Champions League matches, it's always about details.
"At this level, everything is very even and you pay for these mistakes and today it is a hard learning, but it is like that."
Xavi said his team needs to minimise their mistakes.
"There was an error at a corner, there was an error in a transition that we did not stop and they have stopped transitions many times," he said.
"And then what we have failed, we have failed a lot, there has been a lack of effectiveness that we have normally had ... So the way to play was very good, positive for this part, but negative for the result."
