The Serie A champions fell 2-1 behind shortly after the break, but continued to work hard and were eventually rewarded with a late equaliser, much to the the Italian tactician's delight.
"We could have played better after Barcelona took the lead but I'm happy because the team didn't collapse, always remaining in the game until the late equaliser," Allegri was quoted as saying an the post-match press conference.
"We started very well, then later in the game we were forced to defend because Barcelona had possession and it was difficult to press them. However, we did not afford them great chances to score and we also had a few opportunities to get a second on the counter-attack in the first half.
"Our plan was not to allow them a numerical advantage in midfield by pressing when we didn't have to. We also defended well when they were trying to pass in behind our defensive line. We have room for improvement but I'm happy with the way every player helped each other today."
AC Milan resume domestic match action at the weekend with an away game against Napoli on Sunday evening.
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