Hart cemented himself as England No.1. during qualifying for the tournament and has enjoyed a successful season for Manchester City, appearing in every league game as his side won their first Premier League title.
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And former Manchester United captain Neville praised the young keeper, insisting he could prove the difference between success and failure this summer - especially should England face penalties.
“I have been explaining this to some of the lads over the last few days - I went to five tournaments and in four of them we went out on penalties,” he told the Daily Mail.
“I’m not being disrespectful to the goalkeepers who I played with, but we have a great goalkeeper now and that may be the difference.”
Despite highlighting the Three Lions' poor penalty record the Bury-born coach stopped short of using spot-kicks as an excuse for England's past failures.
“That’s not been the real reason. At the ’98 World Cup, France and Brazil were better than us," he added.
“I have analysed it. If you want it in one sentence, we haven’t been good enough.”
The 37-year-old also explained that, unlike in previous tournaments, the presence of wives and girlfriends and their access to the players will be significantly reduced.
“That won’t happen again. The FA learned from the experience in 2006. The England team did. That wasn’t ideal for anybody," he continued.
“It was symptomatic of the times. Between 2002 and 2007 everyone got carried away with everything in life. It is a different world now.
"We are managing it this time in a completely different way. We are here to play football. We are here to work."