The Italian believes that it is essential for his side to score in the second leg at the Camp Nou to kill off the Spanish giants.
"We must score, because Barcelona at home have always scored a lot," he told Sky Sports News. "It will be necessary to have a good match there, probably better than this evening's."
Allegri went on to praise his side, insisting that they were deserved winners and could have scored more goals.
"I think the team produced a big performance. My guys were really good defensively," he added.
"Not allowing Barcelona to score is not easy. In the first half, we had a few chances and we could have done better. But I think my players deserved the win. At the end, we could have increased our lead."
Milan travel to the Camp Nou for the second leg on March 12.