The Essex opener has been given numerous standing ovations during the fifth Test against India at the Oval and the crowd were willing him to go out in style.
The veteran did not disappoint the 19,000 spectators at the south London ground, reaching his 33rd century in 161 Tests in bizarre fashion, courtesy of four overthrows.
The former England captain, about to become a father for the third time, said it was difficult to put his achievement into words.
"It's been the most surreal four days of my life really," he said. "I suppose if she (Alice, his wife) goes into labour tonight that will probably top it off but it's been incredible.
"There's a few of my friends here as well so for that all to happen today and every reception I've had over the last four days it's just been incredible, even that last couple of overs when the whole crowd were singing my Barmy Army (fan) songs, incredibly special."
When asked if it was his best day ever in cricket, Cook described it as a "different day".
"On a purely selfish point of view I couldn't have asked for a better week for me so yes on that side but obviously there have been bigger things in more important games that have meant more."
He said the match had been emotional for him with family and friends looking on, which had brought a different type of pressure.
"To perform and have a day like that I suppose after 160 other games, it's a nice way to go."
The left-handed batsman, who is going to continue to play for his county side Essex next season, said he was not having second thoughts over his decision to retire from international cricket, despite his heroics at the Oval, which have put England into a winning position.
"It's just time for me, it's time for my family and now it makes it even better," he said. "It's always nice people wanting you a little bit more than trying to kick you out and to go out on your own terms (makes it special)."
Cook said he hoped to round off his Test career with a win against top-ranked India on Tuesday, which would give England a 4-1 series victory.
He said retiring from England duty had, in the end, been an easy decision.
"Over the last 12, 18 months things have started to creep into my mind and losing that edge which has definitely happened in training and stuff so that decision was made for me, kind of," Cook explained.
"But it's obviously a big decision because chasing your dreams, playing for England is all I've ever really known."
"When you know it's right, it's right," he added. "This is just the icing on the cake."