Scotland leaders Vern Cotter and Greig Laidlaw refused to blame Joubert's 79th minute penalty for their exit, but questioned why the decision was not sent to the Television Match Official.

Joubert ruled a Scotland player was offside after the ball bounced off Wallabies halfback Nick Phipps' shoulder in a messy lineout recovery.

The decision allowed Bernard Foley to step up and boot the Wallabies to a 35-34 win and advance to the semi-final, but Joubert ran from the field after the final whistle and reportedly narrowly avoided being hit with a flying bottle from the stands.

A distraught Laidlaw asked Joubert to refer the decision to the TMO to ensure he had the correct call.

"I asked him on several occasions what the protocols were. I think you could see by the way that he took his time that he was certainly looking at the big screen. He wasn't sure himself.

"...They go to the TMO for everything else. It was such a big decision, why didn't they go to the TMO for that?

"...I didn't get a chance to talk [to the referee after the game], he left the field too quick. Where I was, I think it was Phipps that jumped and it looked like to me that it went off him. [Josh] Strauss was there as well ... I thought it was an Aussie hand.

"We're not the type of people to blame little things. We could have tightened up in a lot of areas and wouldn't have been in that situation."

Coach Cotter said: "I think we'll take time to review that, have a proper look before we comment.

"I feel for these guys, a tough, tough game. It was fine margins, I'm proud of them. Proud of them as men and as rugby players."

Under World Rugby rules, the TMO can only be called into play for:

The offside ruling does not fall into any category and therefore Joubert's decision on the field stands.

Replays showed Australian replacement Phipps appeared to get a touch on the ball before Scotland prop Jon Welsh instinctively grabbed it while in an offside position.

Joubert could have ruled that it was accidental and awarded the Wallabies a scrum rather than a penalty like he did earlier in the match.

Wallabies coach Michael Cheika did not want to weigh into the referee controversy.

"At the end of the day, as long as rugby's been around, that's what it is. You have to live with the ones you get and the ones you don't. I've become quite neutral on the topic," Cheika said.

"...It's a penalty and that's the way it works. You've still got to kick it."

Joubert was in the action earlier in the second half when he sent winger Sean Maitland to the sin bin for a deliberate knockdown.

Maitland stuck out his right hand to cut off a Bernard Foley pass and had he caught it, he would have raced to the other end of the field and scored a try.

But after intervention from the TMO, Joubert deemed that Maitland deliberately knocked the ball down and gave him a yellow card.

Moments later the Wallabies scored through Drew Mitchell in the spot where Maitland should have been defending and allowed Australia to hit the lead.

Former Scotland captain Gavin Hastings said: "If I see referee Craig Joubert again, I am going to tell him how disgusted I am.

"The referee is not expected to make the right decision all the time. That's what the TMO system is in place for. This is the quarter-final of a Rugby World Cup. This is the highest end of our sport and they have to get these decisions right."

Laidlaw and Cotter were left dejected after their heartbreaking exit from the tournament following a see-sawing battle.

They snatched the lead when outside centre Mark Bennett latched on to a horror intercept pass from prop James Slipper and raced away to give Scotland a two-point lead with five minutes left.

But the Wallabies refused to give in and worked their way down the field before earning a penalty and Foley stepped up to take the shot.

Foley had a mixed night in general play and with his boot, missing multiple shots at goal and struggling to rise to the occasion in the quarter-final pressure test.

However, he showed he had ice in his veins with a shot from 30 metres out and 15 metres in from touch to lift the Wallabies to a one-point win.