Bernardeschi completed his €40million transfer from Fiorentina on Monday and has been handed the number 33 shirt for the new season, despite having worn the number 10 at the Artemio Franchi.
The 23-year-old's move has been compared to that of Baggio, who left Fiorentina for Juve in 1990 for what was then a world-record fee of £8million in a deal that sparked riots from furious Viola fans on the streets of Florence.
Bernardeschi, however, insists he should not be likened to Baggio and admits that he rejected the chance to wear the number he inherited from Michel Platini as he does not feel ready for the responsibility.
"I think it's right and think I have to prove I deserve to wear it," he told a news conference at his official presentation in Turin. "So this year is the right one to show the club, the coach and my team-mates that I can wear it.
"There's no-one like Baggio. In my opinion, comparisons are always wrong. Baggio was perhaps the greatest Italian footballer of all time, he showed that, so I don't think you should compare me to him.
"I'm flattered, but I think it's a bit disrespectful to him."
Bernardeschi is said to have been the target of vitriolic messages from Fiorentina fans since completing his Juve move, while an offensive banner criticising the player was pictured in the city.
The Italy international says it is "unhealthy" to receive such threats on social media but thanked those who have wished him well in Turin.
"I think this is part of an unhealthy society we have in the world today, like fans wishing death or serious illness to people on social media," he said.
"I'm not here to feed this unhealthy part of society. In fact, I thank the fans who, despite everything, wished me good luck.
"Then there are also those who said to me: 'We won't be supporting you anymore but we hope you grow as a professional'. That part of society is healthy and should be supported.
"However, I think the unhealthy part of society should be left alone. I have a strong character so I have no problem. The problem comes when these attacks come on fragile people, and I think that's a problem in society."