Cook, who had come into the match with a total of 83 runs in six previous innings, finished the second day of the fourth Test at Melbourne on 104 not out, having become the first overseas batsman since India's Sunil Gavaskar to record a century on each of Australia's five main Test grounds.
"It was an amazing moment personally after my well-documented struggles," Cook told reporters before the start of the third day's play. "It's frustrating it has come after the series is done, which hurts me even more in one sense, but there is a relief that when it got really tough I managed to dig in and score some runs."
Cook, England's all-time leading Test run-scorer, is playing in his 151st Test at Melbourne, and has not missed a single match in the past 11 years of his career. However, with England 3-0 down in the Ashes, and with his personal form under particular scrutiny, he recognised that he had been under an extra degree of pressure going into this latest innings.
"It's always a test isn't it?" he said. "You have to keep going to the well and digging yourself out of it sometimes, certainly when you bat like me and are never the most fluent. It's hard work and you have to keep doing it.
"There are times when it is tough because you are playing the best cricketers in the world, constantly under some pressure, and some days it is their day. But if you fight through those periods when I went to bed I was proud because a couple of times in my career I have been questioned and been able to respond with some runs."
By the standards of some of Cook's most doughty innings - many of which came on the 2010-11 tour of Australia - this latest century was one of his more free-flowing, featuring a plethora of drives through the covers and down the ground, as well as a final-over gallop to three figures as he capitalised on a loose over of legspin from Australia's captain, Steve Smith.
"When you're averaging 13 there is no point dying wondering," he said. "What is the worst that can happen? You can get a low score and get left out - that's the worst that can happen I suppose - but it's amazing what can happen, more crisp footwork, more intent and suddenly you get away.
"You can forget, when batting, that the first 30 minutes can feel like the longest time, then the next minute you've been batting for four hours. It's a strange sport, it's probably why it drives you mad."
Cook, who turned 33 on Christmas Day, has been the subject of understandable speculation in the course of his fallow tour, with some pundits querying whether he still possessed the drive to keep grinding out the runs in adversity. And while he didn't entirely silence the questions about how much longer he intends to keep going, he has at least ensured that the decision is not about to be taken out of his own hands.
"It's the same as every time people ask me about my future," he said. "It's about trying to score runs to win games of cricket for England. Unfortunately in this series I haven't been good enough and ultimately that hurts because you want to play well in the big games and do something special.
"It's been so frustrating, you do keep asking yourself questions. We haven't played well enough as a team and I haven't scored enough runs in the first three games. Whether it's too late, I don't know - certainly it is for the series - but we've got a chance to win this game, and it was nice to respond with a good score yesterday.
"When it's all done, whenever that is, I can look back on that part of my career and know that when it has got tough I haven't thrown in the towel."