Neville has announced he will leave Goodison Park after eight years at the end of the current season, meaning Everton will be deprived of their captain, and a versatile and consistent performer who has made over 300 appearances for the club.
The 36-year-old is not retiring from the game, but his future plans remain unclear, aside from joining Stuart Pearce's coaching staff for the European Under-21 Championship in Israel.
Brother Gary is both a senior England coach and England's most respected TV pundit, but Moyes says Phil is more likely to pursue the coaching route once he brings his long and successful career to a close.
Meanwhile, Everton have a tough job on their hands in attempting to fill Neville's shoes.
"He's been really influential, Phil,” Moyes told Yahoo!-Eurosport. “He has been a great captain, he has been a great player since he joined us eight years ago, and he will be missed because he is someone I can rely on - on the pitch and off the pitch.
"He is someone I have got no doubt will go on to work in football, and he's someone that we will miss and it will be a hard position to fill because the way he has captained the team has been excellent over the years.
"Phil will be a success whatever line he goes into in life because he conducts himself well, he has looked after himself, he is very articulate in whatever he does - but if I was a betting man I'd say it would be coaching.”
For more from David Moyes, including his views on the future of Marouane Fellaini and the progression of Ross Barkley, watch the full video above.
David Moyes was speaking to Yahoo!'s 'The Dugout' through its partnership with the League Managers Association