The pressure is piling up on Moyes who took over when Alex Ferguson retired at the end of last season. The Premier League title holders have struggled all campaign and lost 2-0 at Greek team Olympiakos Piraeus in their Champions League last-16 first leg on Tuesday.
The Champions League is United's last remaining hope of major silverware this season.
Former Italy and Juventus striker Vialli said under-fire managers in England were allowed more slack than their Serie A counterparts.
"David Moyes, in Italy, would have been sacked three times by now," he told BBC radio. "In the Premier League you get the feeling they give you a bit longer to sort out problems.
"They are more understanding and, most importantly, owners of football clubs don't think they know more than managers.
"They let managers run it for a while and don't just sack you after the first two or three defeats."
This season eight Premier League managers have been dismissed or have left by mutual consent.
In Serie A, 10 coaches have been sacked this term including Massimiliano Allegri who was replaced at AC Milan by Clarence Seedorf.
"In Italy managers are judged simply by results," said Vialli who was in charge of Chelsea between 1998 and 2000 and won several trophies including the FA Cup and now defunct European Cup Winners' Cup.
"Italian managers don't enjoy themselves at all." (Reporting by Mark Pangallo editing by Sam Holden)