In a contentious aftermath to the match, All Blacks coach Steve Hansen accused his Wallabies counterpart Cheika of "hijacking" New Zealand's record celebrations following the Bledisloe Cup finale.
Seething at being dressed up as a red-nosed clown in the New Zealand Herald on the morning of the match, Cheika claimed the All Blacks do not respect the Wallabies.
"They dressed us up as clowns today. They put our crest on it, so they wouldn't want our comment (about the record)," Cheika snapped.
"I don't think they respect our comment, anyway, so we won't make one."
Cheika eventually congratulated the All Blacks for their "outstanding" accomplishment before Wallabies captain Stephen Moore intervened to savage the newspaper, saying he was deeply offended.
"The way the jersey is portrayed in that picture, for everyone that has pulled that on in the history of the Wallabies, I think that's pretty disrespectful," Moore said.
"They won the game so they're the ones laughing, so what do you do?"
Cheika refused to blame the contentious call to overturn a Henry Speight five-pointer for Australia's 37-10 loss to New Zealand on Saturday night but was unable to hide his disgust.
Speight appeared to have locked up the match at 15-all in the 45th minute — with Bernard Foley's conversion attempt to come — only for the television match official to intervene.
Wallabies winger Dane Haylett-Petty was deemed to have changed his line and taken out Julian Savea as his opposite number was pursuing Speight.
The decision left the Wallabies fuming, with the All Blacks rubbing salt into the wound 10 minutes later with an 80m try to Savea against the run of play to turn the Test.
"Obviously I can't say anything because they've got you by the throat," Cheika said after the All Blacks survived a huge scare to notch their top-tier record 18th successive Test win.
"But I've just never seen shepherding from behind before.
"Before any of that, though, we've got to own our mistakes ... before we start talking about the turning point and all that business because we can only call it a turning point if we lose by less than one score perhaps.
"(But) I know there's the ramifications of the game and, at the end of the day, someone's got to own those mistakes as well.
"So we'll see what happens. We'll see if World Rugby comes out with an announcement or anything like that."
Hansen unimpressed with Cheika "sulking"
Though clearly unimpressed, Cheika stopped short of saying relationships between the Wallabies and All Blacks team ranks were frayed.
"They're on top and we're nowhere at this stage. That's the relationship between the teams," he said.
"The thing that got me a bit offside was the accusation (before the first Test in Sydney in August) that we tried to bug them.
"Like, really? Hello. Honestly? ... That's what would cause that bad (blood) for me, that show of lack of respect.
"I wouldn't even be smart enough to get that stuff organised. I'm too busy working on my own team."
Cheika said he would happily share a beer with the All Blacks — but hadn't been asked to.
Hansen, though, insisted there was always an "open invitation" into the All Blacks team room for the opposition and said the All Blacks respected the Wallabies "immensely".
He then accused Cheika of "sulking".
"The paper I saw, he was dressed up like a clown. You've got to be bigger than that, don't you?" Hansen said.
"I've been dressed up as a clown myself. You don't want to take it to heart, otherwise it'll break you.
"We've got no control over what the media do ... the thing for me, this conference tonight seems to have been hijacked by something that's really got nothing to do with rugby, (by) someone feeling a little aggrieved about things that you guys have done, making him be a clown."