The Springboks were outclassed by the Aussies at Suncorp Stadium in Brisbane with the hosts romping to a 49-0 win - their biggest-ever victory against South Africa.
Next up for White's men is a clash with in-form New Zealand.
And although the Boks coach admitted he had work to do in the intervening period, he pointed at the 1998 England team as inspiration.
He said: "England came here and lost by 76 points with a team they were putting together and they ended up winning the World Cup (five years later).
"If we go in with the attitude that we can't (turn things around before next week), then it's going to become even darker for us.
"I take a lot from what happened to that England team that came out here. They got hammered by Australia, they got hammered by the All Blacks, so we've got to get it right."
White also believes the loss of a number of his key players, including flanker Schalk Burger (neck), second-rower Bakkies Botha (calf), centre Jean de Villiers (rib) and fly-half Andre Pretorius (groin), was a determining factor in the rout.
"There's a huge difference between the players we've had in the system for a long time and the next tier player," he added.
"I'm not making any excuses for missed tackles, I'm not making any excuses for execution which I think was poorly done, but it puts things into perspective for me as a coach.
"I thought we'd be a bit more competitive with the team we had here but in all fairness, if you get it wrong on a day like this against a team like the Wallabies, you've got to live with the consequences."
White pointed to the Wallabies' failed tour of Europe late last year as an example of what happens to a class team when they are missing their elite players.
"They know how difficult it is when you go up against a nation who can play, you get yourself behind the eight-ball," he said.