With Vincent Kompany gone and Aymeric Laporte out for six months, Pep Guardiola was forced to play Otamendi and Stones together against Norwich City on Saturday.
The match ended in a 3-2 loss for City, who are now five points behind league leaders Liverpool.
"He (Otamendi) dives in, he has done it all his career," Carragher told Sky Sports Monday Night Football
"He will never change and that's why he's not good enough to play for Manchester City. I have never believed it from day one and nothing I have seen in the last four or five years has changed my mind.
"At this moment, I don't think Guardiola wants to put those two on the pitch together but he has got no option because he has not gone big in the summer."
Neville added that Guardiola's inability to bring a replacement in until at least January could cost City over the whole season.
"Guardiola gave up on this partnership 18 months ago when Laporte came to the club," Neville said.
"Otamendi always gets caught out as a centre-back and quickens up the opposition in attack. He's so not a Pep Guardiola type centre-back, they're usually composed but he's rash.
"Sir Alex Ferguson at times during his Manchester United career would see a game too far with players and say, 'That's it, you're done'. Manchester City's 4-3 defeat at Liverpool in 2018 was the game when Guardiola decided that Stones and Otamendi couldn't play together.
"They've conceded more goals than any other partnership, conceded more goals per game, the clean sheets are down, the three-plus goals conceded is well up and then there's the big one, lower win percentage.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!