The 49-year-old, who was at Chelsea for four years before later managing Watford, thinks that players who do well in the Premier League find it hard to cope with the expectation at major international tournaments.
With the Azzurri first up for the Three Lions in Manaus on Saturday, Vialli is confident that his nation will be in better shape, claiming that they "eat pressure for breakfast".
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"I think that England fans should try to find a balance in between both state of minds but I think the England players find it quite difficult when they play in the World Cup because they are not used to the pressure.
"When they play in the Premiership, when they play Manchester United versus Chelsea, for example, or Arsenal, there's no pressure; it's actually quite fun to play.
"You know that there are no consequences if you don't do well, as long as you do your best on the pitch, and therefore, when they play for the national team, when they wear the England shirt, all of a sudden they realise they are representing their country. They feel there is a massive expectation, there's a lot of scrutiny and a lot of consequences.
"It's the inability to handle the pressure that makes a big difference between between the Italian players and the England players when it comes to the World Cup stage.
"The Italian players, they eat pressure for breakfast so they grow up with a lot of pressure and they know how to handle it.
"Also [Italy] are very good at winning games even though we are not playing at our best, which is something that England players need to learn quite fast if they want to succeed in the World Cup because there will be one or two games where you will not be performing so you need to be able to win it anyway. Historically we are very good at that."
Although Vialli is not convinced by England's ability to perform under intense pressure, he acknowledges that they are more than capable of posing a threat on Saturday.
"I think England are a very exciting side because they have got so many young, talented, creative players playing up front," he added. "The likes of [Daniel] Sturridge, [Wayne] Rooney, and [Raheem] Sterling, [Adam] Lallana, [Danny] Welbeck, they can turn hot quickly and can create problems for the opposition.
"They need to be a bit more clinical, though, because there won't be many goalscoring opportunities so they need to take their chances when they can."