The 48-year-old Italian has bemoaned the lack of finances made available to him by chairman Khaldoon Al Mubarak, who refused to sanction big-money signings such as Daniele De Rossi and Robin van Persie.
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“It’s difficult to say because I wasn’t familiar with the inner workings but I probably would have held tight,” he told talkSPORT.
“There were a lot of players in the team that had only just started to gel and come together. But Roberto always wants to go that extra step and get better and there’s nothing wrong with that.”
The current Premier League champions are 15 points behind rivals Manchester United and with the possibility of a trophy-less season, Cook has supported Mancini despite his precarious position.
“I think all managers are judged by their results,” he said.
“Wherever you set your expectations and your standards is what you are going to be judged on. I brought Roberto into the football club.
"Technically I think he is a very, very strong individual and as a character he surrounds himself with success. There is nothing mediocre about anything he does when it comes to competition. He is a winner.
"It’s nice to have nice people in your organisation, but this is a sport that is judged on results.
“He used to say to me ‘I am judged on how many games I win and how many trophies I win’. I think as long as everybody knows that and understands that, you have to live and die by those values.”
Former City striker Niall Quinn also expressed his uncertainty at Mancini's position, telling Goal.com in an exclusive interview that the Italian could face the chop in the summer if he does not win Monday night's Manchester derby or claim FA Cup glory.