"The Welsh just kept going and going but they couldn't find a way through Australia's defence. The Wallabies just kept finding a way."
Added Gregan: "It was just great grit. True Australian grit. Do us proud. That defence comes from attitude. It's all heart."
The victory may have come at a cost, with stars David Pocock (calf) and Israel Folau (ankle) both picking up injuries, though coach Michael Cheika was confident they would be fit to face world No 9 Scotland in next Monday's quarter-final at Twickenham.
It ensured the Wallabies will avoid South Africa and New Zealand until a potential final.
But it was the remarkable wall of gold, which repelled wave after wave of Welsh attack, which filled Cheika with pride.
In an amazing seven-minute period in the second half, the Wallabies were reduced to 13 men but refused to break - three times denying attacking raids by holding attackers up over the tryline.
"We made some mistakes and we've got so much improvement, but for our courage and the way we put our bodies on the line to defend, I'm very proud of the lads," Cheika said.
"I was very proud of their resilience and their intent to go and do what they did."
It ranks alongside the 11-9 quarter-final win over South Africa last World Cup as the best modern-day defensive effort from the Wallabies.
Genia believed the nature of it, and defending two men down, set it apart.
"This is one of the sweetest ones I've been a part of," he said. "You just had to make a hell of a lot of tackles."
Genia had cynically tackled his opposite Gareth Davies, who had taken a quick tap, before Mumm joined him on the sidelines after grabbing hold of Alun Wyn Jones in the lineout.
Wales No 8 Taulupe Faletau lost control of the ball under pressure from the Wallabies defence as he crossed the line soon after Mumm's sin-binning. Even more impressive was bench flanker Ben McCalman's effort to deny a rampaging George North, who had been brought down by Foley in the lead-up.
The powerful centre was held up by McCalman over the line in a show of strength that kept Australia on top.
The match was all but secured when veteran winger Adam Ashley-Cooper rushed out of the line to shut down another Welsh raid, helping force a turnover.
"That's one of the best wins I've been involved with," captain Stephen Moore said.
"We had to defend with 13 men for a long period down our end and I'm really proud with how we stuck in for each other."
Across the park there were brutal contests for the ball - Pocock, Sean McMahon and Scott Fardy had their hands full at the breakdown up against the Welsh trio of captain Sam Warburton, Justin Tipuric and Faletau.
"We threw absolutely everything at Australia and you've got to give them a heck of a lot of credit," said Warburton.
"Their defence in their 22 was outstanding and we backed ourselves to go for the try. We couldn't get it."
A week after dominating England, the Wallabies' scrum again held firm and they won two first-half penalties to assert its dominance.
Fardy, McCalman and Kane Douglas threw themselves into every contest, with Douglas' 15 tackles the best in the match.
