Cristiano Ronaldo's arrival from Real Madrid in 2018 raised expectation levels at the Allianz Stadium, but despite an impressive debut campaign in Italy, European glory has eluded the Bianconeri once again.
Ajax dumped Juve out at the quarter-final stage 3-2 on aggregate, which has led to plenty of speculation over Allegri's future at the club.
Pirlo, who played for the Italian giants between 2011 and 2015, says his old side are lacking a player like Real Madrid's Isco, with more creativity needed across the middle of the park.
"I think we need an Isco," Pirlo told Sky Italia. "We're on another level, but you have to win the Champions League."
"Allegri has in mind the team of the future for several months and the midfield is the department to be improved.
"Maybe he lacked quality in the middle having bought Ronaldo and didn't know how to get him the ball.
"Midfielders are needed to get to the bottom of the Champions League."
Isco has endured a difficult campaign at Santiago Bernabeu, falling out of favour under Julen Lopetegui and Santiago Solari before Zinedine Zidane's return to the helm in March.
The Spain international was heavily linked with a transfer earlier in the season, but Zidane is reportedly hopeful he will remain in Madrid for at least one more year.
Juventus have, however, already managed to secure the signing of one talented midfielder in the form of Arsenal's Aaron Ramsey, who signed a pre-contract agreement with the club in January.