Trailing 2-1 after the first leg of their semi-final, Juve won 3-0 at Fiorentina thanks to goals from Alessandro Matri, Roberto Pereyra and Leonardo Bonucci.
It was an excellent performance, made all the more impressive by the absence of star trio Carlos Tevez (muscular problem), Andrea Pirlo (calf) and Paul Pogba (hamstring).
Allegri said: "It wasn't easy to win in Florence against an excellent Fiorentina side who found it tough today. Credit to the lads.
"Seasons are decided at this particular moment in time. We're in decent shape from a fitness point of view.
"Hats off to the coaches who get the lads in the right condition. We've also improved our play and move the ball around quicker."
Allegri reserved special praise for Pereyra, who also scored in Saturday's 2-0 win over Empoli.
"He's played a great deal, considering it's his first year at Juventus," he added.
"He's coming on in terms of his goalscoring, possesses great technique and offers unpredictability up front.
"He's got room for improvement, as everyone does, but [he] is already a very important player for us."
