In a meeting between two of Europe's heavyweight clubs, the Italians won at the San Siro through second-half goals from Kevin Prince Boateng and Sulley Muntari.
But Allegri does not think Barcelona are dead and buried ahead of the second leg in Spain on 12th March and believes his team will have to do even better.
Asked how his side will have to perform at Camp Nou, Allegri told Sky Italia: "We must score, because Barcelona at home have always scored a lot.
"It will be necessary to have a good match there, probably better than this evening's."
But Allegri was understandably delighted to defeat Barcelona and was pleased with his players' defending.
He said: "I think the team produced a big performance. My guys were really good defensively.
"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."