England midfielder Barkley has came in for criticism last season and at the beginning of this campaign before he was dropped by Ronald Koeman .
Barkley had re-found his form before a poor Merseyside Derby last weekend saw him slammed by fans and pundits alike.
But a stunning performance against Leicester, including an inch-perfect cross to set up Romelu Lukaku, earned him praise.
Barkley was left out of Gareth Southgate’s Three Lions squad last month is out of contract at the end of next season and risks being sold in the summer.
Neville has taken aim at anyone for writes off the attacking ace.
He said on Sky Sports: “I hope he stays, as an Everton supporter and former player. I hate the people who don’t rate Ross Barkley, it absolutely kills me every time I see someone write or speak badly about him.
“I think you have got to look at the ability of the boy. As an English footballing nation we should be supporting someone with that talent.
“I think he has been the signing of the summer, you talk about Lukaku or losing Barkley, Everton cannot afford to lose him, because there will be clubs sniffing around Ronald Koeman. I think he has that confidence and experience to take Everton up to the next level.”