The Rossoneri lead 2-0 following the first leg at the San Siro but Allegri believes that his team must play better than they did three weeks ago.
"We want to stand up to Barcelona," Allegri told reporters. "I think we will have to perform better than we did in the first leg [if we want to win].
"Tomorrow night we will have to improve. The boys will need to be good in attack and make the most of their opportunities.
"We must remain calm – this is a game like any other."
The draw for the quarter-finals will be made on March 15.