Micheal Cheika

Australia were dumped out of the Rugby World Cup in a 40-16 quarter-final defeat to England on Saturday.

Cheika brought his five-year stint in charge, which included a run to the World Cup final in 2015, to an end after the defeat.

New Zealand coaches Jamie Joseph and Dave Rennie have been linked with the post but, when touching down after flying back from Japan, Cheika told reporters Rugby Australia should look at home for their next appointment.

"I think definitely we should be pushing for an Australian coach," he said. 

Folau sparked a Twitter backlash by revealing he will not support gay marriage, becoming the first high-profile sportsperson to have publicly announced their opposition.

It came after numerous sporting organisations -- including the Australian Rugby Union -- declared their support for a 'yes' vote in the government's postal survey.

Folau's views are also at odds with outspoken former Test skipper David Pocock while current captain Michael Hooper has also voiced his support for gay marriage this week.

The Wallabies were thrashed 54-34 in their Rugby Championship opener in Sydney last weekend, with only a late revival once the All Blacks had already run riot salvaging any pride.

Australia legend Lynagh tore into their performance on Sky Sports, saying their skills were "non-existent".

Cheika's side have the opportunity for revenge in Dunedin this weekend in the second Bledisloe Cup Test.

The Wallabies coach said there is little they can do to alter Lynagh's opinion aside from showing an improvement on the pitch.

Reigning champions New Zealand have been pitted against South Africa and Italy in Pool B, while England have France and Argentina for company in their five-team group.

The Wallabies, meanwhile, will go up against Wales and Georgia, as well as qualifiers from Oceania and the Americas, in Pool D.

But Cheika would not get carried away with what appears on paper to be a better draw, suggesting any hint of complacency could well prove Australia's downfall in Japan.

"When you're standing out there and singing the anthem, 0-0 all bets off," said Cheika.

The Wallabies started the 2016 edition of the competition with two heavy defeats at the hands of the All Blacks, piling pressure on Cheika's squad.

However, they have reacted well with wins over South Africa and now Argentina, leaving them second with two games to play - New Zealand having claimed the title thanks to Australia's 36-20 win on Saturday.

A second successive win had plenty of positives for Cheika, his men racing into a 21-0 lead in the first-half before producing a solid defensive display to ensure victory.