Michael Cheika has refused to announce his resignation as Wallabies coach despite their ignominious dumping from the Rugby World Cup after being outclassed 40-16 by England in the quarter-finals.
Australia had no answer for England, who scored four tries to book England a semi-final berth for the first time in 12 years.
The result on Saturday has almost certainly ended the five-year tenure of Cheika, who's failed to get consistency from his team in the four years since leading them to the 2015 tournament final.
Cheika has said he would stand down if the Wallabies didn't win in Japan, but he was guarded on his future at a post-test media conference.
"I'm being honest. It's a cruel, cruel world nowadays when you're asked those questions two minutes after your World Cup is finished," Cheika said.
"If you'd find it inside you to find a little bit of compassion just to ask more relevant questions... think about peoples' feelings for a minute. Just chill."
Asked if the Australian public deserved an answer, Cheika said: "When the time comes, I'll tell them. They don't need to know today, it's not going to kill them."
England's victory was built on an unforgiving defence and the control of five-eighth Owen Farrell, who kicked 20 points with eight successful shots at goal.
Australia dominated many of the game's statistics, forcing their opponents to attempt 181 tackles to just 78.
However, turnovers and handling errors were a crippling factor against opponents who were methodical every time they made an incursion into Australia's territory.
Cheika again made no apology for his team's heavy ball-in-hand approach.
"Listen, that's the way we play footy. I'm not going to go to a kick and defend game. Call me naive, but that's something we're not going to do."
Australia closed within a point of the lead early in the second half when brilliant winger Marika Koroibete bagged their try, but England muscled up late to score the game's final 23 points.
The result equalled England's biggest ever win over the Wallabies and was sweet revenge for the pool defeat at Twickenham four years ago that knocked them out of the global tournament.
The win was the seventh straight win for England coach Eddie Jones over Cheika, whose erratic approach to selection at the tournament played a part in their lack of cohesion when it counted.
The Wallabies led briefly through Lealiifano's first of three first-half penalties before the game broke wide open through May's double in the 18th and 21st minutes.
The speedy winger's second try summed up the test when a loose David Pocock pass was gathered by Henry Slade, who scooted 40m before a pinpoint grubber was collected with glee by the man celebrating 50 Tests.
Both sideline conversions were slotted by Farrell, who also landed a penalty before the break to put his team 17-9 ahead.
Koroibete's try was set up by smart passing from Reece Hodge and Petaia before the former NRL winger scorched around Elliot Daly.
Just one point clear, England re-established control through Farrell, whose inch-perfect pass sent prop Kyle Sinckler thundering across.
A long spell of Australian attack came to nothing, and England's pack gradually took control, earning three penalties that all turned into three points as well as a late intercept try to Anthony Watson.
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