Juve sealed a seventh successive Scudetto with a point at Roma on Sunday as both they and Napoli kicked off at the same time, but that was not the case in earlier weeks when the pressure appeared to get to Sarri's side.
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.
With one game left to play Juventus can not be caught by second-placed Napoli, which is four points behind after winning 2-0 at Sampdoria on Sunday.
Hundreds of fans gathered at the Piazza San Carlo in Turin waving flags with the number 7 after Sunday's goalless draw with AS Roma sealed another triumph with one game to go after a gripping battle with Napoli.
And their coach believes this had an impact, pinpointing a key defeat at Fiorentina the day after Juventus - beaten by Napoli in their previous match - had conjured up a late comeback against Inter.
Massimiliano Allegri's side also won the Italian Cup in the Stadio Olimpico on Wednesday with a 4-0 win over AC Milan.
"Juventus have a special mentality that has been built up through the years", Di Francesco said. I think it's decisive that they are able to wash their dirty laundry in private and that is something all clubs ought to do, taking this mentality as an example. "Next season, there will be players who will arrive and others who will leave".
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.
It moved a point above Crotone and Spal, which lost 2-1 at Torino.
Emanuele Giaccherini and Roberto Inglese scored in the second half to rally Chievo to a 2-1 win at Bologna.