Michael Cheika urged a reporter to show "compassion" as he objected to being asked whether he intends to step down as Australia's head coach following their Rugby World Cup exit.

Cheika's contract is set to expire and he is widely expected to leave his position, having previously said he would not seek reappointment if the Wallabies did not win the tournament.

However, in a tense news conference after a 40-16 quarter-final loss to England in Oita, the 52-year-old took exception to being asked if he was considering his role.

"It's a cruel, cruel world nowadays when you're asking those questions two minutes after we've been knocked out of the World Cup," said a dejected Cheika.

"If you'd find it inside you to find a little bit of compassion for people who are hurting and just ask a more relevant question [that would be appreciated], because I came here with only one thought in my mind, about winning here. That thought has just disappeared now, not 15-20 minutes ago.

"I know that's what the papers demand, but perhaps, whatever your news outlet is, you should think about people's feelings."

Cheika's future was not raised again until the final question of the news conference. A journalist, who began his enquiry by saying he "appreciated the timeframe", reminded Cheika of his pre-tournament comments about standing aside if Australia did not triumph, asking if that was still his intention.

That query was also rebuffed by Cheika, who swiftly responded: "If you appreciate the timeframe, why ask the question?

He added: "When the time comes, I'll tell 'em [Rugby Australia].

"They don't need to know today - it's not going to kill 'em."