Wallabies coach Michael Cheika quit Sunday after their humiliating 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