Referee Craig Joubert was wrong to award a crucial 78th-minute penalty against Scotland in Sunday's World Cup quarter-final defeat by Australia, says World Rugby.
Scotland led 34-32 at Twickenham when Jon Welsh was ruled deliberately offside for playing the ball after a knock-on by a team-mate.
The governing body said that, because Australia's Nick Phipps touched the ball, "the appropriate decision should have been a scrum to Australia for the original knock-on".
Scotland lost 35-34 after Bernard Foley kicked the penalty.
The statement added that South African Joubert "could not refer to the television match official (TMO) in this case and therefore had to rely on what he saw in real time".
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World Rugby regulations only permit the TMO to rule on foul play or whether tries or kicks at goal are legitimate.
Scotland coach Vern Cotter said a TMO referral "would have taken away any doubt".
Joubert has not been selected to officiate in this weekend's semi-finals.
Frenchman Jerome Garces will referee South Africa versus New Zealand on Saturday and England's Wayne Barnes will oversee Australia against Argentina on Sunday. Both matches are at Twickenham.
World Rugby high performance match official manager Joel Jutge said: "Despite this experience, Craig has been and remains a world-class referee and an important member of our team."
|BBC Radio 5 live rugby reporter Chris Jones|
|"The World Rugby statement is a staggering development. Joubert has been totally thrown under the bus.|
|"It's not a dreadful scandal of a decision but the whole incident has become a total mess by Joubert running off the pitch and World Rugby now coming out and hanging him out to dry."|
Former South Africa captain Bobby Skinstad said the reaction to his compatriot's decision had been "blown out of all proportion".
Skinstad, who won 42 caps, said Joubert had "dedicated his refereeing career to the memory of his father", who was also a rugby match official.
He added: "Craig is a quality individual and a top, top referee.
"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."
Joubert, who refereed the 2011 World Cup final, was criticised for running from the pitch after the final whistle without shaking hands with the players.
Former Scotland captain Gavin Hastings described Joubert's swift exit as the "the worst thing I have seen on a rugby field in a very long time".
Matt Dawson, part of England's World Cup-winning side of 2003, said it was "disrespectful to the game".