The Toffees hammered League Two Cheltenham Town 5-1 on Monday night to move through to the fourth round and Neville suggests the strength of the starting eleven shows Moyes is keen for success in the famous cup competition.
"He (Moyes) wants to win the FA Cup and I think that is a sign with the team he picked," he told ESPN.
"He could have rotated the team. We have a game a week until the end of the season.
"I think he wanted to keep the momentum going. We are on a good run of form, good confidence."