Cook, the England captain, was mentored through the ranks at Essex by Gooch, one of the county's greatest players and England's record Test run-scorer, before working alongside him at international level. (Agencies)
But Thursday saw Gooch become one of the first backroom casualties of Peter Moores's second spell as England coach when he was dismissed as batting coach.
It appeared the 60-year-old former captain, like Cook an opening batsman, was paying the price for England having failed to make the benchmark total of 400 in a Test innings since March 2013 -- a key factor in their recent 5-0 Ashes whitewash in Australia.
Cook, who will captain England in a one-day international away to Scotland next week, said his most recent conversation with Gooch had been one of the most difficult he'd known.
"Everyone knows how close we are -- and we've been through quite a lot together," said Cook.
"To make a decision on a guy I've had so much respect for, and the whole of England has, was tough.
"I was telling a man, who I used to go and queue up to get his autograph and hope he'd score runs, that it's time to move on. I'll remember that for a long time."
"But the caliber of Goochie especially, as a person, he was telling me: 'I totally understand'.
"For him to say that, when a 29-year-old is telling him 'we want to move on', shows just why I hold him in such high regard,” Cook added.
However, Cook insisted he would be happy for anyone in the England side to continue to use Gooch as a personal batting coach.
"I hope that relationship will continue - not just with me," the left-hander said.
"I know Belly (Ian Bell) has used him a hell of a lot, and has had great rewards, and we hope we can continue doing that on a one-to-one basis," Cook added.
"I've worked with him for 11 years like that, and I know that's his greatest strength,” he said.
And Cook said being the bearer of bad news had not damaged his relationship with Gooch.
"We were both very clear we want to remain friends," he said.
"He was immediately talking about other stuff ... how I can go on in my game. That was quite humbling. This is professionalism, and will not affect how we feel about each other,” he added.
Meanwhile Gooch told BBC Radio Five: "I'm not going to think bad of Alastair about this. Playing for England is bigger than the individual and what's right for England is the way forward.”
“I think it's a joint decision -- the captain and coach's decisions have to be pretty much as one. Alastair was in favour of the decision and I respect that,” he added.
"He knows he needs to look at the way he handles a side and stamp authority on a team and making a decision like this is good for him. He has to believe in the decisions he makes. We'll still be friends forever and hopefully I'll still be involved in his game in some way,” he further said.
Cook, the England captain, was mentored through the ranks at Essex by Gooch, one of the county's greatest players and England's record Test run-scorer, before working alongside him at international level.