Fury stopped Wilder in the seventh round of their Las Vegas rematch on Saturday night (Sunday NZT) to claim the WBC heavyweight title and hand the American his first career defeat.
Fury had sent Wilder to the canvas twice and the champion appeared to be on shaky legs when the Brit pinned him in the corner in the seventh round, unloading a barrage of punches that saw the towel come in and forced referee Kenny Bayless to halt the contest.
But Wilder's head trainer Jay Deas revealed in the post-fight press conference that he had wanted to let his charge fight on, and it was co-trainer Mark Breland who had made the compassionate move to spare him from any more punishment.
"What happened between rounds was Mark said something about throwing the towel in and I told him, 'Don't do that', I didn't think he should do that," Deas said.
"Then the fight went on a little bit longer and then I saw the towel go in so I haven't talked to Mark about it but we'll talk about it and figure out what exactly happened there.
"I didn't think he should have [thrown in the towel]. Deontay's the kind of guy who goes out on his shield and he will tell you straight up – don't throw the towel in."
Deas pointed out that the hard-hitting Wilder – who had knocked out every opponent he had faced as a professional apart from Fury – always had the power to turn a fight on its head in an instant.
"You've always got to consider also that Deontay is a fearsome puncher, so that's always a difficult thing because he does always have that [ability] to land a big shot and turn things around", Deas said.
"That's what happened there but Deontay is doing well, he'll be back, he'll be all the better for it.
"But congratulations to Tyson and to his team, a class act all the way around, and we're thrilled to be part of the show with him.
Wilder shared Deas' view that he should have been allowed to continue, saying after the fight that he wished his corner "had let me go out on my shield".
"I'm a warrior, that's what I do. But it is what it is, there's no excuses. We'll come back and be stronger," the battered American said in the ring moments after his crushing defeat.
But Breland – a 1984 Olympic gold medallist and former welterweight world champion – clearly felt it was necessary to bring the one-sided beatdown to an end, a decision backed by most boxing commentators.
Deas attempted to explain the unique dynamic within Wilder's team that resulted in the co-trainer raising the white flag.
"I'm the head coach of the team but we do things a little bit differently, 99 per cent of the time the head coach is also the guy who's lead coach in the corner," he said.
"Ours is a little bit more like an American football team where the head coach doesn't necessarily call the plays – you have an offensive and defensive co-coordinator."
Wilder had to have stitches to a cut in his ear sustained in the third round when Fury sent him to the canvas for the first time with a looping right hand.
Deas admitted that punch may affected his fighter's balance, with Wilder seemingly on unsteady legs throughout the fight.
"It may have affected his equilibrium," he said. "He's going to get a couple stitches there."
Wilder now has 30 days to decide whether he wants to exercise a contractual clause for an immediate rematch with Fury in June or July as the clamour grows for a unification fight between Fury and his British compatriot Anthony Joshua, who owns the WBA, WBO, IBO and IBF heavyweight titles.
Fury would be entitled to a 60 per cent share of the pot in the event of a trilogy fight. Both Deas and Wilder's manager, Shelly Finkel suggested that the 'Bronze Bomber' would seek to set the record straight right away.
"These guys have put on two tremendous fights already, so I certainly think that the public will want it," Deas said. "And I think we'll want it and I think they'll want it, so it seems natural. I think that's what you'll see happen."
Wilder made 10 successful defences of his WBC title, including a controversial split draw with Fury in Los Angeles 14 months ago, which most observers felt the Brit had won despite suffering two knockdowns.