Australia were full value for a 42-17 lead going into the final 10 minutes, but were reduced to an astonishing 11 players following four yellow cards in quick succession as the Springboks' pressure created ill-discipline.
The visitors clawed back 21 points in that period, but ran out of time and paid the price for an error-strewn performance in the first 70 minutes of the game.
"We have nobody else to blame but ourselves for the result," Erasmus told reporters. "We didn't play well enough to deserve the victory. We took a bit of a gamble with some guys who hadn't played together for a long time, but that's not an excuse. The better team won on the night."
Erasmus believed the game was a valuable exercise as his side got a taste of Australia ahead of next year's World Cup and he got a look at players who had not featured in the recent 3-1 series win over New Zealand.
"I know South African supporters will be upset if I sit here and say we're learning a lot while we're losing," he said. "If we'd managed to pull this game through, I would have said we'd learnt a lot about our players and how they respond in tight situations."
Australia remain unbeaten under new coach Les Kiss and the Springboks coach was impressed with their improvement.
"Australia don't make mistakes at the lineout, and they're always organised defensively. There are always numbers on their feet," he said.
"They're a technically very well-coached team. We normally find it difficult against teams that don't miss their roles, particularly around the breakdown."
He added that the influence of Australian rules football on the country's rugby side makes the Wallabies almost a unique opponent.
"I think the influence of Australian rules football and rugby league is evident in their game. They're excellent in the air and they can put those contestable kicks across," Erasmus said.
"They've also got those rugby league running lines where they fix defenders and create opportunities for the players around them. When they get into your 22, they're very direct and difficult to stop."