The loss has almost certainly ended the Wallabies' chances of taking the title.
Although the Springboks must first face the beleaguered Australians in Perth, White admits he already has one eye on the All Blacks while preparing for this weekend's encounter.
"If you beat New Zealand in Dunedin you win the Tri-Nations, it's as simple as that," White told Superrugby.
"I need to check the permutations but I can't see any other outcome.
"But it's not a case of saying because of this result we will win here (in Perth) next week and then take the title in Dunedin a week later. We still want to win as many Test matches as we can.
"We are only going to worry about Perth for now; there is no reason to think too far ahead. I'm not going to water down the result of this Test match because if you look at our results away from home we have not been at our best."
White revealed he was likely to name an unchanged squad for the first time since he took over as coach.
"To win away we need consistency and if that means probably keeping the same team then that's the way it will be," he added.
"In some ways the Wallaby problems put us in a difficult situation because if we start thinking they have so many injuries and they are coming off a tough game we will fall into the same trap we fell into in Sydney (South Africa lost 30-12 earlier this year).
"We have lost 15 away Tests out of 15 against top opposition so we must focus all our energy on winning in Perth.
"The bottom line is simple, though: you win this week in Perth and you win next week in Dunedin and you win the Tri-Nations."