Speaking for the first time since the controversial wicket that lit up the Ashes, Carey detailed how it was a plan to remove the dangerous Bairstow in the fourth innings at Lord's.
He also confirmed he had received an apology from Sir Alastair Cook, after the former England captain perpetuated an incorrect rumour that Carey had failed to pay for a haircut in Leeds last week.
Now public enemy No.1 in England, Carey has copped abuse from fans since the Lord's stumping and been accused of breaching the spirit of cricket by senior figures in the game.
But Australia's wicketkeeper is adamant there was no trickery involved in the dismissal of Bairstow.
"We were switched on to the fact that it was a bouncer plan and it felt like Jonny was pretty switched on to getting out of the way, he wasn't playing any shots," Carey recalled.
"When he ducked, his first movement was pretty much out of his crease. So instinctively I grabbed the ball, threw the stumps down and the rest is history.
"As soon as I got it, I threw it straight away. Once the bail has come off, it's up to the third umpire to deem it out or not out, or the on-field umpires.
"It's been a little bit surprising how it's played out."
Asked if he would do it again despite the blowback from England fans and players, Carey was unequivocal.
"If there was an opportunity to get a stumping, I definitely would," he said.
The 31-year-old said he had learned from early in his career to remain in the crease when batting, after wandering out on debut in Adelaide A grade and being stumped.
Carey blamed himself for that dismissal, a position echoed by Australia's captain Pat Cummins over the past fortnight for any batter who gets out in that fashion.
Carey said he had unsuccessfully tried the ploy as a wicketkeeper in the past, but had never previously been accused of unsporting behaviour.
"My first A-grade game in South Australia, I was out that way," Carey said.
"And when I walked off, I was pretty disappointed. Captain came up to me, he said, 'You'll remember to keep your foot behind the line next time'.
"From my point of view, I wasn't called on it about the spirit of cricket when I tried to do it previously.
"And when I was given out in the same sort of manner, I didn't question it either."
