The Serie A champions tore into Barcelona to win the home league 3-0 one week ago, then gave a defensive masterclass, comfortably containing Lionel Messi, Luis Suarez and Neymar, as they held out for a 0-0 draw in the return on Wednesday.
Allegri, however, said that Juventus could have made life easier for themselves if they had taken advantage of the space Barcelona offered them as the game wore on.
Too often, the Serie A leaders got themselves into good attacking positions only to be let down by a poor final pass.
"Where do we need to improve? In the way we used possession of the ball, especially in the second half," Allegri told reporters.
"They allowed space and we were not very good at exploiting that, even though it should be said that tiredness and defensive energy can make you less lucid when you have the chance to attack."
In general, however, Allegri was not in the mood for nitpicking.
"We should have been calmer and sharper when spreading their play, but it’s not easy to do that here," he added.
He felt that his team, who are unbeaten in the competition and have conceded only twice, could have played all night without letting in a goal and that "only a great Juventus could have qualified against Barcelona."
With an eight-point lead in Serie A and a place in the Coppa Italia final guaranteed, Juventus are still on course for a treble.
That meant there would be no time for celebrations after Wednesday's game - something which Allegri did not even have to spell out to his players.
"It’s the decisive moment of the campaign and these lads have a great sense of duty and professionalism," said Allegri. "We're just having dinner and nothing more. What I like about this team is that there is no need for me to tell them that."
He added: “I am happy with what the lads are doing but the key is not to maintain current form but instead try to improve it."
(Writing by Brian Homewood; Editing by Andrew Heavens)
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