The midfielder insisted his team will not give up on trying to secure a Champions League spot until it is mathematically impossible to overtake fourth-placed Arsenal.

David Moyes’s side have been beset by injury concerns in all areas of the side for most of the campaign.

But they are still only a point behind fifth-placed Aston Villa despite twice surrendering a two-goal lead in Sunday’s 3-3 draw between the sides.

Neville said: “It is an unbelievable effort given the injuries we’ve had that we are still in contention for a European place.

“To be honest with you, I think people are waiting for us to fall now. But you can see the energy in the side and a determination to keep things going.

“The manager has done a great job, making sure we do just the right amount of training, resting us where possible and getting us right for the games.

“He was not happy with just a point at Villa because a win would have taken us above them, but we are still hoping to get into fourth position.

“It is still mathematically possible so we will still keep fighting. No-one is giving up.”

Neville knows Everton will probably have to win their last six matches to have any hope of overtaking the Gunners.

But he is aware Arsene Wenger’s side still have to face Manchester United, Liverpool and Chelsea, which could be Everton’s lifeline.

Neville said: “For us to have any chance of finishing fourth, we need to win all six games and we need Arsenal to lose three of their remaining games.

“Whether that is possible, I don’t know, but we will keep going. Arsenal have got some very tough games coming up and they’ve got to win those as well.

“Let’s just keep fighting and there is not a lot to choose between ourselves and Villa as proven in the three games we have played against them this season.”