The International Cricket Council has admitted third umpire Nigel Llong's decisive decision in the day-night Test was wrong.
Llong ruled there wasn't conclusive evidence to dismiss Nathan Lyon during Australia's first innings at Adelaide Oval.
New Zealand Cricket wanted a please explain from the ICC.
NZ coach Mike Hesson took the issue up with match referee Roshan Mahanama then NZC wrote to the governing body.
The ICC replied on Tuesday, noting publicly the umpire "followed the correct protocol, but made an incorrect judgment".
"ICC has replied to correspondence from NZC relating to the Nathan Lyon DRS review in the 3rd Test," the ICC posted on its official Twitter account.
"ICC has reviewed the decision and acknowledged that it was incorrect."
It will do little to defuse seething NZ players, who could have potentially squared the three-Test series at 1-1 if Llong got it right.
Llong is set to stand in the middle during NZ's upcoming home series against Sri Lanka, where he can expect a heated reception from fans.
Lyon had all but walked off the field during Llong's deliberations, the screen at the ground having shown a big `Hot Spot' on his bat.
NZ skipper Brendon McCullum was shocked his review wasn't successful, as were commentators Shane Warne, Ian Chappell and Ian Healy.
It proved a major turning point in the match, which Australia won by three wickets on Sunday.
Australia would have been 9-118 if Lyon was dismissed for a duck, instead they posted a first-innings total of 224.
Hesson could hardly hide his fury on Monday.
"It was excellent, wasn't it? I think everyone at the ground saw what unfolded," Hesson said.
"It's been spoken about a lot. We've certainly made a representation to the ICC.
"There is a process that needs to be followed with these decisions and we need to make sure that process was followed correctly."
Darren Lehmann felt for his counterpart.
"If I was ... umpiring I probably would have let him keep walking," Lehmann told ABC Radio.
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