The Milan boss was disappointed after a defensive lapse led to Lionel Messi’s equaliser but maintains he was pleased with the Rossoneri’s showing in their 1-1 draw at San Siro
The hosts led through Robinho's eighth-minute strike but Messi levelled matters midway through the first half after being left unmarked on the right.
The point leaves the Italians second in Group H and Allegri was quick to applaud his players for denying Barca the freedom to play.
"The boys played a really well," he said. "We gave Barcelona no room to be dangerous and hit them on the counter.
"We made one defensive mistake and they punished us.
"We created more chances 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 sides meet in the reverse fixture at Camp Nou in a fortnight.