His spirits had improved, however, ahead of the fourth ODI in Perth on Friday.
"That was quite an emotional time - we'd just lost another game," the 29-year-old said at the toss.
"I'm lucky enough to do this job. I'm desperate to carry on now."
Cook has received the backing of the England and Wales Cricket Board to lead the team's rebuilding process despite becoming only the third England captain to suffer an Ashes whitewash.
After losing the last ODI against Australia at home, England have lost nine consecutive matches under Cook, including the Ashes tests.
(Reporting by Toby Davis; editing by Sudipto Ganguly)
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