England arrived for their long tour in November confident of a first series win in Australia since 2010-11.
But they quickly imploded, despite facing a depleted attack missing key quicks Josh Hazlewood and Pat Cummins.
A two-day defeat in Perth by eight wickets and another by the same margin at the pink-ball clash in Brisbane left them reeling and in the firing line at home.
An 82-run loss in Adelaide meant the Ashes were over within three Tests, with England's ultra-aggressive "Bazball" style ruthlessly exposed by the Australian conditions.
Stokes, who was a rare bright spot for England, intends to continue as captain.
"Definitely, I'm as keen as anything to carry on," he said after defeat in the fifth and final Test in Sydney by five wickets.
England at least won the fourth Test in Melbourne to avoid a whitewash.
"I've loved having a challenge thrown at me," said Stokes.
"And at the moment the challenge is getting the team back to where we once were in terms of the performances that we were delivering."
They will face an inquisition when they get home with the England Cricket Board under pressure to act.
Stokes said he expected New Zealander McCullum to still be in the job when they next play a Test in June.
"I do expect him to be, but that's not my decision. If I'm asked my opinion, he'll be getting my full support and backing," he said.
"I absolutely love working with Baz. He's a great man and he's a very, very, very good coach."
McCullum agreed there were "areas to improve" but said he won't be told what to do.
"I will look at it individually and say, 'What could I have done better?'," he told the BBC.
"Am I for being told what to do? Of course I am not."
Whoever remains in the fallout, Stokes acknowledged they had a lot of work ahead of them.
"We could have played much better than what we did," he said.
"The time for reflection is not right now. We've got a long time away to reflect on it. Come June when we next play, hopefully we can put the wrongs right."
Despite the heavy series defeat there were a few plus points for England, who lost fast bowlers Mark Wood, Jofra Archer and Gus Atkinson to injury at various points.
Seamer Josh Tongue came in and was admirable while 22-year-old Jacob Bethell produced a magnificent 154 in Sydney after replacing the out-of-form Ollie Pope.
"Incredible for Beth to get his opportunity in the last game of the series," said Stokes.
"To come out in the fifth game of the series and the way he batted was a terrific effort.
"Josh also put in his best and bowled really well so we have good talents coming through."