"The player was clearly for sale," Cook told BBC Radio Five Live.
"We had entered into a confidentiality agreement weeks ago but, in my personal opinion, they [Milan] bottled it."
As Cook confirmed, negotiations had been ongoing for weeks, with Milan in full knowledge of the significance of their move.
"We had gone through a three or four-stage process in which Milan made it quite clear Kaka was for sale and we made it clear we intended to bring him to Manchester City," he said.
"As we got to the next stage there were questions they could not answer and I think the political and public pressure made them change their conditions.
"We never even met the player. We met his representative, his father, but we had discussed commercial terms only."