Milan head to the Camp Nou with a surprise 2-0 lead from last month's last-16 first leg and if they manage to score in Catalonia, the La Liga giants would need four goals to turn the tie around.
Allegri expects a more aggressive Barcelona side on home soil but warned that with Lionel Messi leading their fightback, a single away goal may not be enough.
"I think it is easy to imagine how Barca will approach the game," Allegri said. "They will press us and not allow us to have much of the ball.
"From our point of view, we know that we will need to score once, even twice, to be able to relax.
"Whatever happens, it will be a difficult match, where we will have to be even better than we were in the first leg.
"We need to defend well, make the most of the chances we do get, and use the ball intelligently.
"If you had told us before the first leg that we would be in this position, nobody would have believed it.
"Even if we score, Barca are capable of getting four goals. But they are also a team that give away a lot of chances.
"If the players remain focused, and we get a little bit of luck, Tuesday can be a historic night for us."