Referee Craig Joubert should have awarded Australia a scrum rather than the penalty which cost Scotland their quarter-final, World Cup officials have said.
Scotland were leading 34-32 when Joubert controversially awarded a penalty to Australia for offside in the 78th minute.
On Monday, the World Rugby match official selection committee said the referee could not have refered the decision to the television match official but should have awarded a scrum.
It said in a statement: "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."
World Rugby High Performance Match Official Manager Joël Jutge said: “Despite this experience, Craig has been and remains a world-class referee and an important member of our team.”
Scots fans were hopeful of a win as they go up against Australia in the Rugby World Cup quarter-final match at Twickenham.
South Africa captain Fourie du Preez broke Welsh hearts today in the 75th minute with a try knocking Wales out of the Rugby World Cup.
The try gave the Springboks a 23-19 victory and meant they booked their place in the World Cup semi-finals.
For a full mach report and highlights visit ITV's rugby page.
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Jamie Roberts has said his team is prepared for "physical warfare" as Wales take on South Africa in the World Cup quarterfinal at Twickenham today.
Wales lost 16 successive Tests against South Africa between 2000 and 2014, but the last two meetings should provide 73 times-capped Roberts and company with cause for optimism.
"The challenge above all else is to get the mind right and put your body on the line for physical warfare," Wales centre Roberts said.
"It is a World Cup quarter-final, and to play in games of this magnitude is what you dream about."
Wales will take on South Africa at 4pm on Saturday.
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Large numbers of England fans will be backing Wales now that their team is heading out of the Rugby World Cup, according to a survey commissioned by bookmaker William Hill.
Of those surveyed, 24% said they would be following Wales for the rest of the tournament.
England are due to play Uruguay in Manchester late on Saturday, in what will be their final match of the 2015 Rugby World Cup, but the fixture has lost much of its appeal for fans since England's defeat by Australia.
Wales, meanwhile, are due to play Australia at Twickenham at 4.45pm, and appear able to rely on a good deal of support from England fans.
Prince Harry turned down the chance to back Wales in the Rugby World Cup following England's early exit.
Asked if, like his brother, he would be supporting the Welsh, who beat England 28-25 in their Pool A match, the prince replied: "There's lots of people to support now."
He also expressed his disappointment about England, saying: "It is a great shame for England but it's still going to be the best World Cup ever."
Prince Harry made the comments as he visited Sandy Park in Exeter for the Pool C World Cup match between Namibia and Georgia.