The Premier League has already advanced funds of £2m to all 68 National League clubs to share but this is money they would have received in August anyway as solidarity payments.
A number of clubs initially thought this would be extra funds and have criticised the move saying it only delays the financial problems they will experience.
Chesterfield have received just under £60,000 as part of their share.
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Neville, 45, the co-owner of League Two Salford City, told Sky Sports' Football Show: “I’ve gone from anger to despair to almost pleading for someone from the Premier League to do the right thing for the game.
“Why am I on calls with chairman of EFL clubs who are desperate to pay their next wages or worrying about their clubs going bust for the sake of a couple of million pounds?
“You hear the National League chairman saying they need £10m to £15m across the 68 National League clubs to prop the clubs at that level up. You've got the FA potentially falling over because of the money lost from their revenue streams.”
The remaining fixtures in the National League season have been cancelled and clubs are now waiting to find out what options will be put forward for how the campaign should be concluded.
The National League board are meeting today to discuss the next steps.
Neville added: “Once the Premier League do the right thing they can be seen as the organisation they should be. We need to fall in love with it again. They need to look after football, reassure the game it's looking after them.
“It's not about the 20 Premier League clubs, it's about the game, it's about the grassroots.
“The Premier League are the only people who can stop this being economic carnage for the game. It's something that should be done very quickly by the Premier League clubs. They can do it, it's just whether they want to do it.”