The Sydney Morning Herald reported that Cheika was picked up on the TV broadcast blowing up and the consensus was that he appeared to call someone on the field "f...... cheats" during the first half.
After the game, Cheika was in no mood to discuss the incident, as highlighted in the video above. He stormed off from the post-match interview, incensed that he was being asked about the outburst.
"What are you talking about? Is that what it's come to?"
Two Owen Farrell penalties gave England a 6-0 lead at halftime in freezing cold and wet conditions which saw both sides struggle to hold on to the ball.
Hooper looked to have scored the first try of the match midway through the first half but he was adjudged to have been fractionally offside after Marika Koiroibete booted the ball down the left touchline.
Cheika sarcastically applauded the decision from his seat in the stands and his mood did not improve when Hooper was sin-binned in the 33rd minute.
It was a record eighth yellow card for Hooper, who was sent to the sidelines for 10 minutes for persistent offside where he was joined by Beale on the stroke of halftime.
Beale was shown a yellow card for deliberate knock-on after attempting, and almost pulling off, a one-handed interception of a cut-out pass intended for Jonny May.
Cheika, incensed, made his feelings known to O'Keeffe at the interval after coming down to the touchline and could find himself in hot water with World Rugby for his actions.
Reece Hodge's kick cut the deficit to 6-3 but England extended the lead in contentious fashion after turning defence into attack.
A magnificent scything run from Wallabies centre Samu Kerevi bisected the English defence but Tevita Kuridrani spilled the offload with the line at his mercy.
England halfback Ben Youngs booted the loose ball down the field looking for touch. Despite video footage appearing to show the ball grazed the line, Elliot Daly's try was awarded after he scampered past Beale to touch down.
The Wallabies fought back well with Foley kicking a penalty after a strong spell of pressure but the game swung in England's favour in the 70th minute.
A superb break from Marika Koroibete saw him exchange passes with Stephen Moore and he appeared to get the ball down under a cluster of bodies.
However, after a lengthy video review, England were awarded a penalty after Moore was adjudged to have impeded England's Chris Robshaw.
The decision knocked the stuffing out of Cheika's side and England ran in three late converted tries through Jonathan Joseph, May and Danny Care to add some gloss to the score.
