Controversial former Wallabies head coach Michael Cheika says he should have quit before last year's Rugby World Cup instead of calling it quits after his side was dumped out of the tournament at the quarter-final stage.

Cheika, who resigned shortly after Australia's 40-16 mauling by eventual runners-up England, told The Times he should have stepped aside after Rugby Australia (RA) hired former Scottish international Scott Johnson as director of rugby early in 2019.

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Johnson was brought in following an extensive review of the Wallabies' dismal 2018 season, with a three-man selection panel introduced soon after.

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While Cheika admits he didn't agree with Johnson's appointment, he remained confident that the Wallabies could win the World Cup - despite a string of underwhelming performances and calls for his head to roll.

"In a footy team there can only be one boss, that's all there is to it. I should have left because that shows they [RA] didn't trust me any more," Cheika told The Times.

"I loved Australian rugby and I thought I could do it, I believed I could get the players together and I didn't want to let the players and the supporters down.

"I tried to manage it the best way I could without being out of order. If you cause turbulence at that point, everyone feels it and I didn't need everyone to feel the turbulence in the team. You have to deal with it internally."

The 53-year-old former Waratahs No 8 quit a few days after the Wallabies' World Cup exit, revealing he had "virtually no relationship" with RA's former CEO, Kiwi administrator Raelene Castle.

Castle, who had previously led Netball New Zealand and became the first female chief executive of a club in the NRL when appointed to the role with the Bulldogs in 2013, stepped down in April following several turbulent months.