The former striker, who played on both sides of the Manchester divide but is best remembered for his successful spell at United, has made his bold claim despite the Blues' rise to joint top of the Barclays Premier League table.
Cole said: "Every other week someone is coming out saying they are not happy. You can't run a tight ship like that. You don't see it at Manchester United, Arsenal or Chelsea."
Victory at West Ham saw Mario Balotelli substituted to stop him getting himself sent off - followed a day later by confirmation that Carlos Tevez wanted to leave, triggering a downward spiral in the club's relationship with their captain.
A strongly-worded statement released by the South American on Sunday night revealed that his relationship with senior City officials - believed to be chief executive Garry Cook and football administration officer Brian Marwood - had broken down beyond repair.
City are privately indignant of such claims, questioning exactly what Tevez's issues are given his much-publicised anguish at being separated from his two young daughters.
It all paints a pretty sorry picture, which Cole is convinced will lead to their championship challenge fading.
"There are a lot of problems there," he said.
"Anyone who has any common sense and understands football knows that.
"You can't have disputes with the manager at such regular intervals."