Australia coach Robbie Deans has hailed the bravery of matchwinner James O'Connor, whose late penalty dethroned world champions South Africa.
The Wallabies set up a semi-final showdown with New Zealand at Eden Park after O'Connor sent his 71st-minute kick between the uprights.
It capped a fine performance from O'Connor, the right winger who belied his slight frame to withstand everything the Springboks could throw at him.
"James showed a lot of courage defensively in his tackling, but he also showed a lot of courage in the air," said Deans.
"No doubt a lot of the South African approach was targeted at him. He not only stood up to it, but he also had the last say.
"He wanted that. He was looking forward to that opportunity to kick that goal.
"It's a great sign, it's a great trait in a competitor."
Australia will monitor the fitness of Kurtley Beale and Pat McCabe closely over the coming days after the duo sustained hamstring and shoulder injuries.
"Kurtley was tight. We're confident he hasn't torn his hamstring but we'll know more in 48 hours," he said.
"Pat was also talking up his physical state in the changing room, but once again we'll know more in the next day or two. He's a very willing man."
The defeat marked the end of an era for South Africa with grizzled veterans John Smit and Victor Matfield now entering international retirement.
Australia captain James Horwill admires their longevity and insists they will be missed in the Test arena.
"They're two excellent servants, not only of South African rugby but also world rugby," said Horwill. "They're guys that have given their all to their provinces, to their country. They'll be sorely missed by the teams that they're leaving.
"Both of them have played over 100 Test matches and anyone who does that in today's age, it's a huge effort."
South Africa scrum-half Fourie du Preez insists the demise of the Springboks' World Cup defence is difficult to take.
"It's much harder to accept when you think about all the hard work you put in. To pull up short is heart-breaking," he said.
"It's been a long road for us and it's a sad exit."