However, he accepts his future is "up to other people" after losing the Ashes in just 11 days - and the immediate task is to state his case by salvaging something from the tour in the remaining two Tests.
The New Zealander had branded this Ashes as "the biggest series of all our lives" but has seen his hopes of delivering the urn evaporate after humbling defeats in Perth, Brisbane and Adelaide.
McCullum's predecessor, Chris Silverwood, did not survive a 4-0 thrashing four years ago and questions are already being asked about who should carry the can for the latest defeat Down Under.
McCullum is keen to pick up the pieces from a desperate trip and be part of the rebuild but understands that his fate lies in the hands of others. Managing director of cricket Rob Key sits above him in the chain of command, but is facing tough questions over his own position, with chief executive Richard Gould ultimately responsible for the next steps.
Asked if he would still be in charge at the start of the English summer, he said: "I don't know. It's not really up to me, is it?
"I'll just keep trying to do the job, try to learn the lessons that we haven't quite got right here and try to make some adjustments. Those questions are for someone else, not for me.
"Sometimes you don't win, and then those decisions are up to other people. It's a pretty good gig, it's good fun. You travel the world with the lads and try to play some exciting cricket and try to achieve some things.
"I don't do anything to protect the job, for me it's a matter of trying to just get the very best out of the people and try to achieve what you can with them. I'm enjoying the time that I've got with these guys and I think we've made some progress from when I took over to where we are.
"We're not the finished article, but I think we've definitely improved as a cricket team. We've had an identity about us.
"You're always looking at what you've got right and what you've got wrong, and you're not too ignorant to admit that you get some things wrong. (It's OK) as long as you don't keep making the same mistakes."
There are two more games left, starting in Melbourne on Boxing Day before moving on to Sydney for the New Year Test. Lose both and it may become impossible for any of the key decision-makers to hold off the tide.
That means they are anything but dead rubbers for a management team and a squad looking to save their international careers.
"Now's the time for us, in the last two Tests, to really show our identity," McCullum said.
"What I'm trying to achieve with this team, and what the skipper's trying to achieve, is to try and finish this tour with some pride salvaged from what's been pretty disappointing so far.
"I'll always have the back of my players, and always support them, and I'll always make sure that I'm protective of them as well in a public forum. That doesn't mean you don't challenge privately, but in a public forum, you're always protective.
"I wouldn't imagine anything would change in the coming days as we look to try and salvage something from this. I have conviction in the style of cricket that I try to get the teams to play, with the players that you've got who are suited to it."
