The hosts secured an eight-wicket victory over Cook’s men to move into a 4-0 lead in the current series Down Under.
I’ve got no plans of going anywhere
The 28-year-old has struggled to find form, like most of his team-mates, in Australia despite their 3-0 win on home soil in the summer.
But Cook is determined to continue in his captaincy role and help oversee England’s resurgence after a disastrous series.
“I 100 per cent want to carry on,” Cook said. “In a strange way I’m enjoying the job.
“I’m totally responsible as captain for the team, and if at the end of the series the selectors decide I’m not the best man for the job then so be it.”
Cook added: “It would hurt, and I’ve got no plans of going anywhere.”
Cook, however, admitted that his captaincy has played a part in their heavy losses in Australia.
“Yes. It’s something you do look at as captain and leader of the group,” he said.
“I think we’re preparing in the right way, but just not delivering it out there – or Australia aren’t allowing us to.”