A disconsolate Michael Cheika hailed his Australia players as "a credit to their country" after the Wallabies were dumped out of the Rugby World Cup at the quarter-final stage by England.

Despite starting superbly in Oita, the 1991 and 1999 world champions were ultimately thumped 40-16 as England defended superbly before pulling clear in the second half.

Australia head coach Cheika is widely expected to leave his role, having failed to oversee a repeat of the team's run to the final in 2015.

The 52-year-old cut a distraught figure in his immediate post-match interview, but he made a point of highlighting his team's commitment to the cause.

"I think the lads put everything they had into it today," said Cheika. "I want all the Aussies at home and over here to know that. They gave it everything; they put their bodies on the line.

"We made a few mistakes at different times, but they've given everything, these lads ... and they're a credit to their country."

Australia had more possession throughout Saturday's contest but could only manage one try, through Marika Koroibete, while England crossed four times courtesy of Jonny May (2), Kyle Sinckler and Anthony Watson.

"I thought we actually played quite well, especially the first 50-60 [minutes]," Cheika reasoned.

"We gave away two intercepts and they [England] defended well like you've got to, so the better team won.

"That's the way it is, you've got to suck that up sometimes. I was supposed to get this done for the people here and for Australians. I'm so disappointed."

Wallabies skipper Michael Hooper added: "We're really upset. We emptied everything into this and we didn't get it done, which is pretty gutting for a lot of reasons.

"Firstly, there's a lot of our guys who are leaving. Secondly, we had a great supporter base over here to push us along and we really felt it along the way. To not be able to do it for them and ourselves is pretty gutting."