Wallabies coach Michael Cheika quit on Sunday after their humiliating Rugby World Cup quarter-final exit against England, drawing the curtain on a five-year reign that started strongly but ended in criticism and disappointment.

The 52-year-old, whose contract expires at the end of the year, had previously indicated he would not reapply for his job if they failed to win the tournament.

After testily refusing to comment on his plans in the immediate aftermath of their 40-16 defeat to Eddie Jones' England, Cheika confirmed it was his last game in charge.

"I put my chips in earlier in the year, I told people no win, no play," he told reporters in Oita.

"So, I'm the type of man who is always going to back what he says and I knew from the final whistle but I just wanted to give it that little bit of time to settle down, talk to my people and then make it clear."

Glasgow Warriors coach Dave Rennie, a New Zealander, is seen as among the front-runners to replace him.

Cheika, who narrowly avoided the axe after a horror season last year when Australia won just four of 13 Tests, had come under fire from domestic media Sunday over his tactics in the tournament.

The Sydney Telegraph said he had taken the Wallabies backwards, with his planning "exposed as a failure", while Fox Sports Australia claimed there was "passion without intelligence".

Cheika insisted he would "have loved to stay on", but would not go back on his word.

"I'm attached to the team and it's been an honour to do this role to coach of Australia," he said, adding that he had no immediate future plans. 

"It's not given to a lot of people and I have taken it with a lot of pride and honour. I made my call and I wanted to show I was prepared to put myself on the line to achieve what I believe the team could do.

"I can honestly say I'm always looking to be better but I am really proud of what I have been able to do over the last four years with the team under some very challenging circumstances on and off the field."

Australia's World Cup exit was a bitter end for eight squad members who are either moving to overseas clubs next year or retiring, including centurions Will Genia and Sekope Kepu, along with flank David Pocock.

Cheika's tenure was marked by a successful 2015 World Cup campaign in which Australia reached the final, only to be beaten by the All Blacks. It earned him the world coach of the year accolade.

But the past 18 months have been less successful, with last year's miserable run followed by the disappointing World Cup in Japan.

His powers had been watered down at the end of last year, when Scott Johnson was recruited from Scotland to assume the new role of director of rugby - effectively his boss.

And in a bombshell on his departure, Cheika revealed he barely had a relationship with the Rugby Australia hierarchy.

"It is no secret I have no relationship with the CEO (Raelene Castle) and not much with the chairman (Cameron Clyne)," he was quoted as saying by Australia's Fox Sports.

In a statement, Castle thanked Cheika for his "dedication and service".

"Michael is a passionate and experienced coach who worked tirelessly to get the best out his players," she said, adding that Johnson would now lead a full review, with much work already completed in "preparing for the future".