The Italian champions travel to Camp Nou on Tuesday for their Group H blockbuster, with Ibrahimovic returning to his former club.
He will be keen to strike fear into the opposition after leaving Pep Guardiola's men last year, but the shooting has already started as Allegri sounds an early warning to the European champions.
"Ibrahimovic is very important for us. Last season he did tremendous things, especially in the first half of the season," the coach told uefa.com.
"We won matches thanks to him when we were not a team yet. We were on our way to becoming a team, and Zlatan made the difference.
"How do you take on Barcelona? Good question. They are a difficult side to play, but you have to try to give your best technically, tactically and physically.
"I think that with [Antonio] Cassano, [Zlatan] Ibrahimovic, Pato and Robinho we have world-class players in attack."
However, the outlook is not completely bright as the club's Champions League ambitions ended in failure last season after crashing out against Tottenham in the last 16.
"The lesson we learned was that in the Champions League you cannot afford to make any mistakes," said Allegri.
"So next time we play a match like that we have to be better prepared."
Milan play Lazio in Serie A on Friday night ahead of their trip to Spain.
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