Llong ruled there was not conclusive evidence to dismiss Nathan Lyon during Australia's first innings at Adelaide Oval, when his attempted sweep-shot was caught, despite infra-red imaging system Hot Spot showing a big mark on the bat.
Lyon then went on to contribute to a 74-run partnership which helped Australia to a first innings lead. New Zealand eventually lost the test by three wickets in a close contest.
New Zealand Cricket had asked for a 'please explain' from the ICC.
NZ coach Mike Hesson took the issue up with match referee Roshan Mahanama, before NZC wrote to the governing body.
The ICC replied, 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. Black Caps skipper Brendon McCullum was shocked his review was not successful, as were commentators Shane Warne, Ian Chappell and Ian Healy.
Australia would have been 118 for 9 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.
Source - radionz.co.nz