Milan headed to Camp Nou on Tuesday looking to defend a 2-0 first leg lead in their UEFA Champions League last-16 encounter, but ran into a Barca side on top of their game.
Lionel Messi inspired the hosts to a 4-0 victory in Catalunya, with Milan unable to cope with the constant pressure they found themselves under.
Allegri was forced to concede afterwards that his side struggled to contain Barca and that they must now focus their full attention on the battle to return to Europe's premier club competition next season.
He told Sky Italia: "I think Barcelona played a sensational match for the first 30 minutes in the first half.
"They shot two times with Messi and then (Christian) Abbiati stopped them. We then hit the post through (M'Baye) Niang and on the counter we conceded a second.
"We are sorry for the loss, for the club, for the supporters and for the guys who hoped to do well.
"Our team can grow. I am happy with how my players have performed. We are disappointed but this experience will be useful for the future.
"Now our aim is to get to the Champions League next season. This match must allow us to grow."