The Wallabies came within a whisker of avenging last week's comprehensive 54-34 defeat to the All Blacks before a last-minute Beauden Barrett try swung the tie back in New Zealand's favour in a pulsating 35-29 result.
The match started late after the Wallabies complained their buildup had been affected by a floodlight failure.
"I've got to tread lightly here", Cheika said when pressed to explain why he was baffled by some of the refereeing decisions.
"We've got to let our game do the talking tomorrow, that's it".
"A more dominant team would have finished the job and that's something we can improve on", skipper Kieran Read said.
A frustrated Michael Cheika said it is not acceptable for Australia to be seen as a "gallant loser" after a heartbreaking loss to New Zealand and questioned Nigel Owens's officiating in Dunedin.
There was that brilliant strip on Williams close to the try line in the second half, but don't forget the thumping tackle on Williams minutes earlier.
The seesawing contest continued from there, and sustained pressure eventually told as Ben Smith found space on the outside and New Zealand pinched the lead back.
Beale was nearly Australia's hero, scoring a try in the 76th minute with blood pouring down his face, before New Zealand finished the job from the ensuing kick-off thanks to a match-winner from No.10 Beauden Barrett. "Number one I can say, because it was clear to everyone, is [Retalllick] has picked one of our blokes up and put him on his head".
If they are to have a chance of at least preventing another breakout by the All Blacks, the Wallabies will have to do much better in defence.
Australia: I Folau; D Haylett-Petty, T Kuridrani, K Beale, H Speight; B Foley, W Genia; S McMahon, M Hooper (c), N Hanigan; R Arnold, R Simmons; A Alaalatoa, S Moore, S Sio.
Australia pushed out to a 17 -nil lead but that could have easily been 24-nil if Foley had been able to kick more than one from four. Soon after though, they were sprung, as Aaron Smith snuck through from the base of a scrum to bridge the gap to three points at the half.
"It's a real thing you've got to keep with all this professionalism and everything, is just about getting that in there".
Genia made a brilliant individual break for his try, beating Ardie Savea and McKenzie, but Foley missed a vital conversion.
After Beale's try, the All Blacks seemed down and out but again found the capacity to rebound, instantly making the winning try for Barrett.
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