The Scot, whose contract expires at the end of the season, has agreed a six-year deal to become Sir Alex Ferguson's successor at Manchester United.
After 11 years at the club, where he has regularly had the Toffees punching above their weight, Neville believes Moyes deserves to take the plaudits.
"With the events of this week for Everton, for me personally, the manager, players, supporters and chairman, it will be one of those special days we remember for the rest of our lives," said the 36-year-old, whose eight-year association with the club will end next weekend.
"Forget my situation, just in terms of the celebration of the manager and his achievements it is going to be an unbelievable day and one I can't wait to be involved in.
"I am actually a little bit glad (the attention will be on Moyes) in a way. I don't want any fuss, I've not deserved the fuss, I've just been a player.
"Better players than me have left this club and have achieved more than me at this club."