Moyes has hailed the 33-year-old as ‘exemplary’. Neville is on the verge of his 200th appearance for Everton.
“He has been exemplary since he has been here as a professional and as a player,” said the Scot.
“Coming from Manchester United, a lot of people might have seen it as a step down but I think he saw it as a step up.
“He has grasped the opportunity, he has brought leadership and a winning mentality. He doesn’t half take the ball and take responsibility. Even when it is not going right he still wants it, that is a great trait to have.
“He plays every game as if it is his last and is really disappointed when he is not winning or doing well.
“He has a lot of things that are difficult to teach people and the way he prepares himself for every game is a credit.”