Ex-City club captain kept his enthusiasm in check for the disgraced former CEO, who oversaw his sale to Aston Villa in 2009
Dunne, who served the Citizens for nine years between 2000 and 2009, was allowed to leave the Etihad during Cook's tenure at the club. The former CEO had infamously said 'Richard Dunne doesn't roll off the tongue in Beijing' prior to the player's departure.
Cook resigned his post at Eastlands last September after evidence emerged of abusive emails being sent to a player's mother.
"The club is better off without him and they'll progress even further without him," Dunne told the Irish Mail.
"I don't pay any attention to people like him. It doesn't matter (what he said) because he doesn't matter. The club has benefited from not having him around and if they do win the league they're going to flourish and get even better."
The Dubliner was a fans favourite during his long stint with the club, earning the supporters' player of the year accolade on four occasions. Big-spending City have gone on to win the FA Cup and stand on the brink of a first Premier League title following Dunne's departure in 2009.
"You can't be looking back wishing and wondering," said Dunne on the club's fortunes since he left three years ago.
He added: "I don't think I should be there or think I could be there. It's hard, I enjoyed my time but it is different now. It's just part of football where it's time for people to move on."
Dunne's old club won the Manchester derby 1-0 on Monday night and can secure the crown with victory in their final two league games.
"I think it's inevitable that City will win the league eventually and once they do and they start winning trophies it will then be more acceptable for the real, real big players to move to a team like that," concluded Dunne.