Cook also admitted that he feared for his place in the team after a lean run of form in the Ashes series.
The former skipper scored an unbeaten 244 to break another record, Viv Richard's mark of 208 as the highest score by an overseas batsman at the MCG.
Speaking after play on day three Cook revealed his frustration at not being able to influence the Ashes series.
When asked if he thought he might get axed Cook said: “You don’t know, do you?
“I would have been entitled to be…just because I literally hadn’t scored a run since Edgbaston.
“It was very frustrating.”
There is almost a sense that Cook has taken on board a little too much of the criticism fired his way during his time in the Test team.
Speaking of his progress up the all-time runscoring ranks he said: “I can’t really explain that, I probably feel a bit sorry for Brian Lara.
“(But) it’s obviously a special moment to see your name up there.
“Most of my runs are pretty ugly runs – quite hard work.”
Cook admits to struggling with self doubt for almost his entire career telling the post-play press conference: “I’ve doubted myself for 12 years – and I’ll probably continue to doubt myself.
“Obviously the longer it [a bad run] goes, the harder it becomes.
“So I suppose that’s why I’m quite proud…going to the well again and delivering a performance like that.
“It’s just a shame it’s three-and-a-half to four weeks too late. I’ll have to live with that for a long time.”
