Pietersen hit out at the Zimbabwean, claiming that he tried to rule by "fear", and was critical of his man-management of the team.
However, Cook has insisted that a large portion of the Three Lions' success in the four years of Flower's tenure was down to his coaching methods.
"I've known Andy since he was a player in the Essex dressing room," Cook told BBC Sport.
"He took me under his wing as a player and then, obviously, your relationship changes as a coach to a player and then to a head coach and a captain.
"I've only got respect for him, as a man, as a coach. Chatting to some of the other players about it, they feel the same. A lot of our success was down to his drive and his determination to make us a tough England side."
Cook also admitted that he felt that Pietersen's book had "tarnished" the team's success under Flower.