After five years in charge as head coach, Cheika announced on Sunday in Oita, following Australia's 40-16 quarter-final loss to England, that he would not seek a new contract after a tenure which saw the Wallabies win 34 of 68 Tests.

On Saturday, Cheika said it was "cruel" for reporters to quiz him about his future following Australia's biggest ever World Cup defeat but a day later, after speaking to his family, he confirmed the news everyone expected.

Before the World Cup, Cheika was on record saying that he would walk away if the Wallabies did not lift the Webb Ellis Cup.

"Obviously I got asked the question in the press conference about what is going to happen going forward and at the time I wasn't keen to answer but I always knew the answer in my head," Cheika said. "I wanted to speak to my wife and tell a few people I care about because I put my chips in earlier on in the year and I told people no win, no play. I knew at the final whistle but I wanted to give it that little bit of time to settle down and talk to my people.

"I made the call. I'm a calculated gambler in that regard. I have no regrets about making the call. I'm attached to the team and it's been an honour to do this role to coach of Australia. 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. In five years of being in charge I have loved it ... so [there is] no emotional toll. I'm no drama queen. I love the ups and downs and that's the way she rolls."

Rugby Australia conducted a review late last year following an international season which saw the Wallabies win just four of 13 matches - their worst calendar year on record.

Cheika survived the review but attack coach Stephen Larkham was sent packing. RA appointed Scott Johnson as a director of rugby but despite toeing the party line all year, Cheika said the power shift was tough.

"I think it's no secret that I pretty much have got no relationship with the CEO and not much with the chairman," Cheika said. "Scott's a lovely bloke and I get on fine with him but I'm not really into that type of thing. I like to take responsibility. I found that a little bit difficult at times, yeah, but it's tough because you can't always do how you want it. That is the way the role is set up and I know my place within that structure."

Meanwhile, Cooper, who played under Cheika at the 2015 World Cup but has not been selected for Australia since June 2017, let his feelings known on Twitter.

Replying to a tweet from former England player Ugo Monye about Cheika's resignation, Cooper wrote: "If he actually cared about Aus rugby he would have done it a while ago."

New Zealander Dave Rennie is understood to be RA's top target to replace Cheika but there are other potential candidates.

England coach Eddie Jones is under contract until the end of 2021 but is understood to be looking at options beyond the World Cup, including tier-two nations such as Fiji.

New Zealander Jamie Joseph, the Japan coach, is also under contract with the Brave Blossoms but must be considered an attractive prospect given his team's stunning performances over the past four weeks.

Ireland coach Joe Schmidt has already indicated he plans to stay in Europe after the World Cup. His appeal is likely to have diminished, however, after Ireland's dismal World Cup campaign, which saw them beaten by Japan in the group stages and monstered by the All Blacks in the quarter-finals.

Of the Australian Super Rugby coaches, only Dan McKellar could be considered a realistic contender. He has not won a major title with the Brumbies, however, and is likely to be groomed for a role in the national set-up post-2023.

Since the last World Cup, the Wallabies have won 23 of 52 Tests for a winning record of 44 per cent.

Cheika said he intended to see out his contract until the end of December and was happy to help with a review if required. "I'm sure there will be debriefings and working out who to take over next," he said.

He also said the selection of 19-year-old Jordan Petaia at No.13 for the England quarter-final was very much his and he had no qualms taking risks throughout his time in charge.

"When it comes to these things, even when you look at the selection of Jordan last week, I knew that would be something he could handle and I was prepared to take that even though some people may have worried about it," Cheika said. "It certainly turned out to be a success I think.

"I put my chips in and I didn't get it right. I had full trust in the players they would get it done. It didn't happen ... that's the way she rolled. We weren't able to deliver consistently over the whole time."