Cook believes that the need to have a fresh start following a difficult few months on tour was behind the decision to ask his batting mentor leave the England setup.
"To be the guy who rang him up to tell him we're looking to freshen up the coaching staff was incredibly tough for me personally," the 29-year-old told BBC Sport. "He's a great man.
"But we have made the decision which we think will benefit the England cricket team. There has to be some freshening up - otherwise you get stuck in the past."
The ECB have not yet announced who will replace Gooch on a full-time basis.