Allegri admitted that his side were punished for their one defensive mistake of the night, but was happy to maintain a two-point lead over Celtic in Group H.
"The boys played a good game, giving Barcelona no room to be dangerous and hitting on the counter," he told reporters after the match. "We made one mistake defensively and they punished us.
"We created more chances tonight than in the match we won last season, but this is a good result because we still have a two-point advantage over Celtic."
The two teams meet again at the Camp Nou on November 6.