City moved above Manchester United last weekend after a home win over Newcastle that followed the Red Devils' failure to overcome Sunderland at the Stadium of Light.
It means Roberto Mancini's men are currently the closest challengers to champions Chelsea, with the prospect of even more money being spent by owner Sheikh Mansour should they remain in contention by the January transfer window.
United have not been used to sharing top billing in Manchester for over two decades, and City have not won a trophy of any description since 1976.
But Neville feels his club have to take the Blues' threat seriously now.
"Last weekend's results mean we are now behind Manchester City in the league, which hasn't happened too often in the past 20 years," Neville told the Sunday Times of Malta. "There is no doubt that we have to see City as major challengers this season along with Chelsea.
"At the moment, City and Chelsea are above us and the money that City have spent, and the quality and depth in both squads, means we have to see them both as rivals for the title."
United resume their quest for supremacy against West Brom at Old Trafford next Saturday.
Yet it is away from home where the Red Devils need to improve.
Sir Alex Ferguson's men are yet to win on their travels and may come to regret throwing away victories at Fulham and Everton.
Certainly, Neville views those draws - and the one that followed at Bolton - with greater regret than the Sunderland stalemate.
"In games when we miss chances or we are on top and we get a draw then we are disappointed, but we didn't deserve anything more than a draw in the Sunderland game," he said.
"There is obviously some concern about our away form because we have played four and drawn four.
"The difference between getting one point and three is significant - it is the difference between us being sat alongside Chelsea at the top of the league and being five points behind.
"We can't have any complaints about drawing 0-0 at Sunderland, but against Everton, Bolton and Fulham we could and should have done better."