Moyes signed Neville from Manchester United eight years ago.
He said: "He's certainly been a big part of the progress we've made.
"We needed a different type of player to come in. We got Phil and I think he's surpassed what I thought he could do.
"He could play at full-back or in midfield and that gave us opportunities to be versatile with him.
"His leadership qualities, as I've said before, have been excellent.
"But he's seen the change in the team and quite a few players come and go. He's been one of the main players with the likes of Tim Cahill, Leighton Baines and Phil Jagielka that have been with us for most of that time."