Juventus put up a valiant fight in Berlin, only to be undone by Barcelona’s attacking power as Luis Enrique’s men ran out deserved 3-1 winners.
The Italian giants will have to be content with the Serie A and Coppa Italia crowns at the end of a wonderful season, and Allegri hopes there will be more to come.
He told Sky Italia: “We were naive on the Barcelona goals but we fought until the end. It was a fantastic season and I cannot say anything negative about my team.
“We risked a lot and had several chances. But when you play against great players, you sometimes think you’re in control and when you think you have it, the opponents score.
“Maybe we can do some things better but we played the game until the end. Now we want to establish ourselves among the best eight European teams.
“The first objective is, as always, to win Serie A and the Coppa Italia. The Champions League remains a dream.”
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