Blues manager Mark Hughes was sacked and immediately replaced by Roberto Mancini despite having lost less games than any other Premier League club and having reached the Carling Cup semi-finals.
O'Neill, whose side face Arsenal at Emirates Stadium on Sunday, said: "Manchester City had lost less games in the Premier League than anyone else.
"I can accept the fact that they may well have drawn some games they should have won.
"But this idea that you step in and be given some money to spend and you turn things round immediately, just wouldn't happen in any other business.
"It wouldn't be accepted in any other business.
"There should be some sort of parallel drawn with football but we accept now there is isn't and there is no such thing anymore.
"I've heard there was talk the manager (Mancini) had been speaking to City some weeks before.
"Mark Hughes had taken the team into the Carling Cup semi-final, the first visit they had made there for 20 odd years, and so it (football) can be pretty fickle."
O'Neill is optimistic striker Emile Heskey could be fit to play some part in the festive programme after fears he faced a long lay-off with a groin problem have been allayed.
Heskey limped out of the weekend home win over Stoke midway through the first half but concerns he could be side-lined for five to six weeks have proved unfounded.
O'Neill said: "Emile went for a scan. It shows a little bit of something but he is feeling much better and I think it is going to be a short-term injury.
"He may be available for one of the two games against Arsenal and Liverpool over Christmas. That in itself is half decent news for us.
"There were suggestions that he may be out for five or six weeks, and it was kind of worrying when he came off, but I would be confident enough to say that is not the case."