Stones, 22, is one of just three specialist centre-backs in Roy Hodgson's England squad for Euro 2016 and will arrive at the tournament following a season blighted by several high-profile errors for his club.
Former Toffees captain Neville is well acquainted with the impact a major mistake can have on a player's career - as a 23-year-old, the defender conceded a last-minute penalty that saw Romania eliminate England from the European Championship in 2000.
But the ex-Manchester United man has insisted Stones is capable of fulfilling his considerable promise and urged the skilful youngster to continue playing his natural game.
"He has been heavily criticised and a lot of it has been absolutely scandalous and personal - it's as if we are trying to destroy the kid," Neville was quoted as saying by the Mirror.
"He's been criticised for overplaying, but that's rubbish - for me, if he stops taking the ball, that's when I would be criticising John Stones.
"Some of the criticism he's had has been scandalous from ex-players, who didn't have half the ability he had. I'm talking about players that couldn't pass the ball or control it in tight spots where you have to have composure.
"They say you should defend, first and foremost. But Stones can defend and he can also play football. This kid is going to go right to the very top and instead of killing him we need to back him."
"The only thing that worries me is that we have to cut out the individual errors," he said. "That's the only thing that has punished the team.
"And that's what Roy has got to sort out. He has to drill into them – cut out those individual errors."