The Rossoneri’s 2-0 advantage from the first meeting in Italy was wiped out by half-time thanks to a Lionel Messi double, before second-half goals from David Villa and Jordi Alba put the tie to bed.
The match could have been much different had M’Baye Niang found the back of the net instead of the post, minutes before Messi made it 2-0, and Allegri maintained that the game was always likely to be decided by such small margins.
“Of course, qualification was always going to be a matter of centimetres. We hit the post with Niang, then conceded with Messi,” lamented the 45-year-old trainer to reporters.
“In order to play these games, you need legs and I made these choices. If Niang had scored, my choice would’ve been praised. Luck was with us in the first leg with that deflection into Boateng’s path, this time it went against us with Niang hitting the upright.
“This defeat is disappointing for the club, the fans and the lads, as they gave their all and hoped to achieve something remarkable. Tonight it was tough, yet we kept it open to the end and when 3-0 down had some chances that could have gone better.
“Barcelona are the strongest side in the world. Messi and Iniesta kept dribbling with such cool heads in stoppages, Xavi was so sharp. I have to praise my lads for not giving up to the very end, as they could’ve let their heads drop."
With Champions League football no longer a concern for the rest of the campaign, Allegri encouraged his side to focus on qualifying for the competition next season, with Milan sitting in third place in Serie A.
He added: “On Sunday we face Palermo and our position in Serie A is the most important thing. Our objective right now is to get back into the tournament for next year.
“We had five players in their first Champions League campaign. Tonight’s game will help everyone grow. It will be a useful experience.”