Juventus, crowned champions for a seventh time in a row, could have sealed their success with victory but were unable to break down their 10 men opponents at the Stadio Olimpico.
It gave Juventus a four-point lead over second placed Napoli and gave 50-year-old Allegri his fourth Cup and league double in as many seasons with Juventus.
Roma's Radja Nainggolan saw red in the 68th minute, but the capital outfit held firm against the Champions, who secured their 34th League title.
Sarri repeated his complaint that Juventus habitually played their matches before Napoli.
Allegri's side also won the Italian Cup in the Stadio Olimpico on Wednesday with a 4-0 win over AC Milan. Meanwhile, they might be one of Europe's most successful teams, but it's more than 20 years since they were crowned champions of Europe.
Massimiliano Allegri has finally spoken on reports linking him with a move to England, saying he will remain at Juventus unless the club fires him.
A number of players could leave Juventus at the end of the season, notably club captain Gianluigi Buffon, although the veteran goalkeeper has yet to confirm his retirement.
Arkadiusz Milik curled a delightful effort into the top left corner in the 72nd minute, seconds after coming off the bench, while Raul Albiol headed in a corner eight minutes later.
Despite the impressive result, Crotone slipped into the relegation zone, below Spal on their head-to-head record.
Fiorentina are eighth, three points back of Atalanta, and will need to win and overturn a seven-goal difference next week to earn a spot in Europe.
"We played after Juve 14 times in the last 16 rounds and seeing as Juve pretty much always win, that badly damaged us".