Hughes's 18-month spell at the club came to a brutal end when he was sacked after the 4-3 victory over Sunderland, with former Inter Milan coach Mancini immediately named as his successor.
"It seems to me there is an overwhelming theory there is a conspiracy," Cook told reporters on Monday.
"The owner, the board, the management team, made a decision, we moved quickly as was expected and like any other business we had a plan and we moved to work on that plan."
Cook has been criticised for the way the sacking was handled and was only due to read a pre-written statement on the matter when Italian Mancini was introduced at a news conference on Monday.
While City's statement said the club opened talks with Mancini on Thursday, the Italian indicated he had met chairman Khaldoon al Mubarak two weeks before and Cook was drawn into a verbal response.
"Two weeks ago Roberto met Khaldoon al Mubarak in London and after the Spurs game (a 3-0 defeat last Wednesday) he was contacted for further discussions on a more serious nature," said the chief executive.
"The discussions in London were general, they were about football and they were considering managerial options at that point.
SUCCESSFUL CLUB
"There are no conspiracy theories, we are working hard every day to make this a successful football club. We need to draw a line and move on to the future," added Cook.
He was also asked whether Hughes should have been sacked before the Sunderland match.
"The decision was made on Thursday, the chairman had to jump on an aeroplane because he was adamant not to make a phone call, send a fax or a text or an email and he wanted to do it in person," Cook said.
Quizzed on whether he had met the chairman, Mancini added: "Yes, two weeks ago in London. I met Khaldoon two weeks ago. He's a fantastic man and the other men that work in the club are fantastic.
"We met for this situation because he wanted to speak about football generally and Inter. He's a great person."
The statement read out by Cook said big-spending City's decision to look at other potential managers was made after the 1-1 draw with Hull City three weeks ago, one of seven successive draws which stalled City's excellent opening to the season.
The statement also played down talk of the players being angered by Hughes's sacking.
"There is no player rebellion," it read. "The staff are going about their business today as usual."
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