Manchester City have been told they must recruit in the January transfer window to ensure they compete for both the Premier League title and the Champions League.
The Blues struggled their way through a tough test on the road at Everton but ended up winning 3-1 at Goodison Park.
Gabriel Jesus opened the scoring in the first half for Pep Guardiola's men but Dominic Calvert-Lewin equalised before the break.
Ederson went on to deny both Calvert-Lewin and Yerry Mina before City struck with goals from Riyad Mahrez and Raheem Sterling.
Guardiola's side remain five points adrift of Liverpool in the race for the Premier League title but after a hard-fought win on Merseyside, Neville insisted that City have to sign a centre-back in January to compete for silverware both at home and abroad.
"It's never ideal to spend in January but you have got to think City are thinking about dipping into the transfer market for a centre-back," Neville told Sky Sports. "They bought (Aymeric) Laporte last year in January and they are going to have to do something similar again.
"This won't be good enough for the Champions League and the Premier League. He'll (Guardiola) know it. He knows the standard better than anybody.
"I saw that he (Guardiola) said they have no money. They have got more than everyone else. They have set limits.
"Maybe it's not the actual fee but it's more than actual wages which have been demanded by players that is making the Man City hierarchy nervous. They want to stay within a structure.
"With (Vincent) Kompany it has left a huge void. There are not too many of him around and he's difficult to replace."
