"I thought we played a lot of footy in the end but we but we got penalised a lot didn't we?" Cheika fumed.
"(It was a) 13-3 penalty count and that costs you field position, costs you territory and obviously points as well.
"You can't win a Test match if you're giving away that many penalties or that big a difference between the two teams. Impossible."
Cheika made it clear he would be taking his concerns through the official channels before next week's season-ending Test against England at Twickenham.
"That's something I'll be dealing with Alain Rolland about afterwards," Cheika said.
"I'll go through the proper channels as opposed to making it an issue out here and see if we can get something but I doubt it."
It was an inspiring victory for Ireland - who lost star flanker Sean O'Brien to a leg injury hours before kick-off, and were also without key playmaker Johnny Sexton, with the win completing their first-ever trio of victories over the southern hemisphere's big three.
Australia had been thoroughly outplayed before a Dane Haylett-Petty try right before the break gave them hope and a 17-7 halftime deficient - while further five-pointers to Tevita Kuridrani and Sefanaia Naivalu briefly gave them the lead.
But it wasn't to be, as Michael Cheika's men became the latest Wallaby side to fail to emulate the grand slam feats of the 1984 side.
In the first half, behind an 8-1 penalty count, the Wallabies enjoyed a meagre 28 per cent possession and 23 per cent territory in a hopelessly one-sided half in which flanker Dean Mumm spent 10 minutes in the sin bin for lifting the legs of Irish prop Tadgh Furlong in a ruck.
The Australians were punished immediately, as Ireland lock Iain Henderson finished off a classy team try to take a 10-0 advantage.
The Wallabies were unimpressed with Ireland's second try, where centre Garry Ringrose split the defence and was rewarded with a five-pointer despite hints of obstruction.
The halftime break refreshed the Wallabies, and soon enough centre Kuridrani was the beneficiary of some slick hands in the backline to score out wide.
After trading penalty goals, Australia went ahead for the first time in the 58th minute through a converted try to winger Naivalu, who hit a gap and crossed for his first Wallaby try.
A penalty goal to Foley - who would be yellow-carded in the dying moments for a dangerous tackle - extended the lead before Earls reclaimed it for good for Ireland with 14 minutes remaining.
- AAP
