The result left them facing a World Cup quarterfinal against a resurgent South Africa.
Had they won, Wales rather than Australia, would be facing Scotland - on paper an easier opponent - in the last eight.
Now they are up against the two-time World Cup champions South Africa.
Wales, however, beat the Springboks 12-6 when the teams last met in Cardiff last year.
"We've got a quarterfinal against a side we beat last time," said Warburton, whose side will face South Africa at Twickenham next Saturday.
"One thing this group of players doesn't mind is a challenge and that's what great teams are made of," the flank added.
This was Wales' 11th straight defeat by Australia, with Wallaby flyhalf Bernard Foley kicking five penalties to two from Welsh counterpart Dan Biggar.
Australia were down to 13 men midway through the second half after Will Genia and Dean Mumm had been sin-binned.
Yet even then, Wales could not score a try.
"You've got to give them credit. We were hungry for that try but we have to give them credit. If you spend that much time in their 22, you have to come away with a try," said Warburton.
Wales coach Warren Gatland added: "It was courageous defence by Australia. They were throwing their bodies on the line.
"It was a tight, tough Test match, not a lot in it. We were held up over the line three times and had opportunities but didn't take them," the New Zealander added.
"But the guys have already turned their minds to South Africa, the focus is purely on winning a quarter-final."
