Despite going ahead 2-0 in the first half, the Catalans slipped to a 2-2 draw after two defensive errors, and the 31-year-old was furious.
"We made two foolish mistakes in defence and they cost us dearly," Xavi said to his club's official website.
"[They were] two isolated errors. From there on, their confidence grew and they showed more aggression than us.
"We weren't expecting it," he continued. "We had the game under control until then and were looking to finish off the job."
Pedro agreed with Xavi's assessment, admitting: "We had got the game on track in the first half but then we let in two goals and things became complicated. We should have scored more after making it 2-0, and we had chances to do it."
Dani Alves was also in agreement, but chose to focus on their upcoming UEFA Champions League fixture against AC Milan.
"It's hard to explain, but two mistakes cost us the match. It was a good wake up call. We have to be more careful," he said. "Football has been tough to us today, because they equalised with the only two chances they had.
"We're not panicking, but we know that to repeat our successes we have to repeat what we did before, and that's not easy, and luckily, we have a very entertaining game on Tuesday."
Despite breaking Barcelona's record of number of appearances, Victor Valdes was sombre.
"It has been a rather odd day," he admitted. "I'm happy to have beaten Zubizarreta's number of matches, but I'd prefer to have won."
"They got two goals to tie the game. Was it to our discredit or their credit? A bit of both, That's part of the game, and it shows nothing is easy. You have to concentrate for 90 minutes because it's no good to dominate the whole first half but not the second.
"We had it all under control in the first half, playing well from the back, and holding onto possession, but now we must think about the Champions League," he concluded.
Manager Pep Guardiola hoped that his players would learn from their mistakes.
"We had a good first half, to get to 2-0, and in the second we were okay but in football you know that the level of workrate should always remain high, especially in La Liga," Guardiola said to Sport.
"What is clear now is that this season, we will have to perform better than the last if we want to win again," he added. "When you win, it becomes harder [to repeat your achievements]."