City were taken over by the Abu Dhabi United Group for Development and Investment and immediately splashed out a British record £32.4million to sign Robinho from Real Madrid.
Yet despite the money and influence of their billionaire Arab investors, Cook states Hughes will still have the final say over playing matters and squad make-up.
Cook told the club's official website: "Mark talks about moving the club forward and we could not have a better vehicle for doing that.
"We should not forget that the club has moved forward considerably over the last two years, and he is excited to be in this position, every manager would like to be in that position.
"He has made it quite clear to everybody outside the club that he runs the football side of the business, and he is anticipating nothing changing from that.
"There is no reason for that to change, he is far more knowledgeable about football than all of us!"
City have been linked with multi-million-pound bids for a number of players since the Abu Dhabi takeover on Monday.
Cook admits it is a highly exciting time for the club but is determined to keep everyone's feet on the ground.
He added: "Manchester City is in the news for all the right reasons at the moment, and everybody is very excited at the club.
"People may talk about the dynamics changing, but staff at the club are still working very hard and Mark is back coaching the team as normal.
"We would like to see great players at the club, because that's what moves the club forward, but we have to be realistic on a day-to-day basis.
"Maybe we have taken our eye off the ball a little bit, don't forget that we have one of, if not the, best youth team in the country at Manchester City.
"Mark's coaching team are committed to that model, we talk about superstar talent but you should never take away from the fabric of the club, and that is developing the youth players."