Former captain Cook, who enters his final Test on Friday, hit a low in 2014 when KP was axed after a 5-0 Ashes defeat.
He said: “It was the toughest time of my career and there’s no doubt it affected my batting.
“The day Andrew Strauss came out and said Kevin wasn’t going to play for us any more, that was a massive weight off my shoulders.
“I was involved in the decision at first but the England captain doesn’t have the final say on hiring and firing.
“I agreed with it but said, ‘Why don’t we give him some time off, we can go away and maybe KP can come back later on’.”
But England managing director Paul Downton wanted to axe Pietersen immediately and, when the issue flared up again the next year, new chief Strauss slammed the door for good.
Cook took a torrent of abuse online, while Pietersen wrote a savage book in which he trashed many England team-mates and members of the management.
Speaking to Test Match Special, Cook added: “I haven’t spoken to him since that day but time is a great healer.
"We spent a lot of time together and created some amazing memories. The thing is, we never fell out.
"Since then, the internet has fallen out for us.”
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