An emphatic 3-0 victory at Fiorentina allowed Juve to progress to the??Coppa Italia final with a 4-2 aggregate win.
Juve had lost 2-1 in the opening leg in Turin but hit back with goals from Alessandro Matri, Roberto Pereyra and Leonardo Bonucci.
“I thought the team interpreted this game very well,” Allegri said to Italian TV station Rai Sport. “It’s by no means easy to win away to a Fiorentina side who have been playing great football.
“I am delighted with what my players did. It’s a big achievement to overturn a difficult result.
“To win in Florence and not concede a goal is not easy. We played a balanced game, showing good technique and great personality. We deserved to go through.”
The victory was all the more pleasing for Allegri considering his side were without injured Carlos Tevez, Andrea Pirlo, Paul Pogba and Stephan Lichtsteiner.
“I’m very satisfied with this performance,” he said. “We had many top players out injured but those that came out on the pitch did a great job.”
Juve, who have not lifted the Coppa trophy since 1995, are well on their way to their fourth straight Serie A title.
They are also in the quarter-finals of the Champions League.
Fiorentina coach Vincenzo Montella was hugely disappointed.
“We didn’t put in the performance we wanted,” Montella said. “Juventus deserved to win.
“We knew we were facing a very good side. They were clinical and took all of their chances.
“My side continued to fight hard until the final whistle. At times you just have to acknowledge the other team were stronger.
“The Serie A table shows how far ahead Juventus are from the rest, so evidently that’s still the case.”
Juve are 14 points clear of Roma at the top of Serie A and will face either Napoli or Lazio in the Coppa final on June 7 in Rome.
Napoli host Lazio on Wednesday with that semi-final tied at 1-1.