The Hoops slumped to a 3-0 loss in the first leg of the last 16 clash, leaving little hope of rescuing the tie in Turin.
Celtic boss Neil Lennon hit out at Spanish referee Alberto Undiano Mallenco and his officials afterwards for their reluctance to punish the Juventus players for their handling of the home players in the box.
Asked about the match officials, Vialli said: "I think the Italian defenders carry on a very bad habit they have developed in the Italian championships, where referees are very reluctant to award penalties for that kind of behaviour in the penalty box. Because of that, Italian defenders behave the same way in Europe.
"They've got to be extremely careful because there were definitely some situations where there should have been penalties awarded for Celtic in my opinion.
"There is a very thin line between what you can do and what you can't do. Some pulling is allowed but you need to be clever. But yesterday was far too much in my opinion."
According to the former Juventus and Chelsea striker, attention back in Italy has centred on the display of the team, rather than the referee.
He said: "Everybody has been concentrating mostly on the Juventus performance, which we all thought was terrific against very worthy opponents. I totally agree with Lennon, I think that Celtic were very good, they played very high tempo, but we thought were extremely good."