The two sides played out a 1-1 draw at San Siro on October 22, and Allegri has challenged his players to stand up to the daunting test of facing Barca on their home turf.
"Playing against Barcelona brings great motivation to anyone. It will require the perfect performance," Allegri told reporters.
"It will require a great performance, both physically and psychologically, both in attack and defence.
"We need to be wary, but also have courage to play and do even better than in the first leg. Last year our 4-0 defeat here was our worst game in recent campaign."
Milan were beaten 2-0 by Fiorentina on Sunday.