World Rugby has admitted referee Craig Joubert blundered by awarding Australia the last-gasp penalty that sent Scotland crashing out of the World Cup.

The Wallabies clinched a dramatic 35-34 victory at Twickenham on Sunday when Bernard Foley was on target from the kicking tee with 43 seconds remaining.

World Rugby has said in a statement that having reviewed the incident, the "appropriate decision was a scrum to Australia for the original knock-on" and not a penalty.

The admission by the game's governing body that one of their most respected referees effectively cost Scotland a place in the semi-finals will provide scant consolation to Vern Cotter's men.

The Scots were magnificent as they fought back to establish a 34-32 lead in one of the World Cup's greatest knockout matches, only to be robbed of a famous victory by Joubert's pivotal late call that provoked a furious response from former players of all nationalities.

World Rugby failed to explain why Joubert sprinted down the tunnel after blowing the final whistle, but it is understood that the official wanted to avoid any heated discussions on the pitch with devastated Scottish players.

The refereeing appointments for this weekend's semi-finals are due to be announced on Monday night and Joubert is not expected to be one of the two officials chosen.

World Rugby's statement explained the sequence of events that denied Scotland a last four appointment with Argentina at Twickenham on Sunday.

"The selection committee confirms that Joubert applied World Rugby Law 11.7 penalising Scotland's Jon Welsh, who had played the ball following a knock-on by a team-mate, resulting in an offside," the statement read.

"On review of all available angles, it is clear that after the knock-on, the ball was touched by Australia's Nick Phipps and Law 11.3(c) states that a player can be put on-side by an opponent who intentionally plays the ball.

"It is important to clarify that, under the protocols, the referee could not refer to the television match official in this case and therefore had to rely on what he saw in real time.

"In this case, Law 11.3(c) should have been applied, putting Welsh onside. The appropriate decision, therefore, should have been a scrum to Australia for the original knock-on.

"Overall, it is widely recognised that the standard of officiating at Rugby World Cup 2015 has been very high across 44 compelling and competitive matches to date."

Scotland great Gavin Hastings viewed Joubert's action in dashing off as "despicable", former captain Andy Nicol branded the South African a "coward" and retired England scrum-half Matt Dawson tweeted "Craig Joubert you are a disgrace and should never referee again!!"

However, a groundswell of support was building for Joubert led by former South Africa captain Billy Skinstad.

"I know Craig very well. He has a man of unquestionable integrity and is a fantastic referee," Skinstad told Press Association Sport at the Beyond Rugby event in central London.

"Craig is a very tough guy and a good guy. His background is a lot more complex than people realise.

"His father Des was an outstanding referee and made a decision from a young age to take up refereeing full time. He made such an impact on so many schoolkids' lives and he was bit of a legend in the Kwazule-Natal area.

"Des passed away from cancer and Craig has dedicated his refereeing career to the memory of his father.

"Craig is a quality individual and all the stuff around the decision has been blown out of all proportion.

"I'd feel really sad if any of this has got to him as a person given he has given so much to the game."

Australia coach Michael Cheika also came to the defence of the beleaguered Joubert.

"No one's congratulating Joubert for picking up the tiniest knock-on before we scored the try in the corner and going back to the TMO. Some decisions you'll get and some decisions you won't," Cheika said.

"Someone threw a bottle at him when he was leaving, didn't they? I'd be racing off too if I saw a bottle coming. I don't think anything of him going off quickly.

"I don't like the way that people are making something out of the way he ran off the field."