Carey's controversial stumping of Bairstow is back in the spotlight this week, with the play the centre point of the third instalment of The Test documentary series.
One of Australia's best in England until that point in the second Test, Carey later fell into a lean patch that extended into the home summer before an end-of-season resurgence.
The wicketkeeper's run of outs included scoring 109 runs at 15.57 in his next seven Test innings, as well as being dropped from the one-day side during the World Cup.
Carey's teammates - including Steve Smith and Usman Khawaja - raise concerns over the treatment of Carey from English fans and media during the documentary.
But the man himself said he had largely been sheltered at the time, only now realising the full brunt he copped from critics.
"I understand maybe the correlation between the stumping and being left out of the one-day squad," Carey told AAP ahead of the release of The Test on Friday.
"Unfortunately my form maybe fell away slightly after. I felt like I got some good scores in between some low scores.
"I thought throughout the summer I got some good 30s and a couple of 50s. That's just a matter of batting and pushing on with them.
"And I got some starts that would have been nice to go on with them. But that's cricket as well at times. You sort of ebb and flow a little bit.
"But I never felt like there was any impact on field from that dismissal."
Alex Carey trudges off after his dismissal at Old Trafford during the 2023 Ashes series. (AP PHOTO)
Carey also insists he would not change anything about the play to dismiss Bairstow at the crucial moment during England's run chase at Lord's.
One of the main revelations in the documentary is that Cummins instructed Carey to pull off the stumping, something not noted publicly at the time.
But Carey wants it to be clear that several players had the same idea, while watching Bairstow walk out of his crease after ducking deliveries.
And as the wicketkeeper, Carey has no issue with Cummins not putting his hand up immediately to say the call was on him.
"You play professional sport for the big moments. You want to play sport and play it in a way it's remembered. And that will be," Carey said.
"A few guys recognised it ... there were a couple of other guys in the ring.
"To have Pat recognise it as well and signal it, we knew what Greeny was going to bowl.
"(For me) to pick it up cleanly and throw and hit the stumps, it all played out exactly how we would have liked it to.
"Then you have 11 blokes celebrating pretty hard after it was given out, it was pretty cool to be out there."
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