The England number one made a high profile error that led Crystal Palace’s equaliser on Saturday before Everton rallied to win 3-1 at Goodison Park.
There have been calls for Pickford to be replaced in the England goal by Manchester United goalkeeper Dean Henderson, who has emerged as one of the best players in the league this season while on loan at Sheffield United.
Pickford, who starred for England at the 2018 FIFA World Cup in Russia, made four errors leading to goals last season and he has already made two more in the current campaign.
Neville criticised Pickford back in September after the former Sunderland shot stopper was seen laughing as Everton lost 3-1 to Manchester City.
As the pressure continues to mount, Pickford has hit back at the naysayers, reserving a special mention for the former Manchester United captain.
"I think the press and everybody; the punters - look at Gary Neville - they just want to come for England players," he said.
"Everyone gets stick. Some get a lot more praise than others. That's part of being an England player.
"Everyone hates you, for some reason. I just get on with it. You have got to live with it, you have got to learn. I know what I am capable of and I know what I am good at.
"It is what it is. Look at Joe Hart when he was number one. He got pelters every week.
"You just keep it away from your head as the only person who can sort things out is yourself as an individual, on the pitch and in training.
"It's looking after things on the pitch for Everton that is my main aim. That gets you picked for England.
"It's funny because everyone raves about you when you are with England but then you get back to your club and everyone wants to slate you.
"As a person, I don't let it affect me. But it does p*** you off."
