The Italian coach spoke highly of the Catalan side ahead of Tuesday's match and said he has not had enough time to prepare for the crunch encounter
The Serie A giants travel to Catalunya knowing that a victory or a score draw will see them progress in the competition after a goalless stalemate in the first leg at San Siro.
Speaking to reporters at Milanello after the team's flight to Barcelona was delayed, Allegri noted that the Blaugrana have the edge and admitted that his side have not prepared for the match properly.
"We have not had too much time to prepare for the game tactically because we have been playing every three days," Allegri said.
"We will do it tonight in Barcelona. In any case we played against them just last week and we are ready.
"Barcelona are still the best side in the world, but there will be some crucial moments tomorrow night that we have to make the most of. I expect Barca to be at their best.
"I am not going to think too much about the final score, it could finish 0-0 and go to penalties although I doubt that will happen."
Saturday's 1-1 draw with Catania has left Milan just two points clear of second-placed Juventus, but Allegri has called on his players to switch their focus to the continental clash.
"The team must not think about the mistakes at Catania," the 44-year-old coach said.
"We are going to Barcelona to play a game that is worth a semi-final spot in the Champions League and we have to only think about that.
"The Scudetto can wait for a few days."
Alexandre Pato could make his first appearance for the club in over a month after being named in the squad for Tuesday's match, but Allegri still has doubts about the Brazilian's fitness.
"I saw Pato yesterday for the first time in a month, he trained for the first time with the squad," he added.
"He will conduct his second training session tomorrow and then I will see."