The world champions, fielding a heavily rotated side, trailed by 25 points with little more than a quarter of an hour remaining.
A late surge, fuelled by Australia's collapse in discipline that left the Wallabies with just 11 players on the field at one stage, brought the Springboks within four points.
"It's sh*t to lose for us, we don't enjoy it. We know how South Africans feel now and we don't want to give them that feeling," Erasmus said.
"For us, we lost in a Springbok jersey against Australia, and with all the disruptions, we have nobody else to blame but ourselves for the result."
He acknowledged minor technical issues during the match but shut down any suggestion that external factors decided the outcome.
"I know the technology failed a bit, the clock kept running and didn't stop at times for example, but that didn't influence how we played. We controlled that," he said.
"We didn't play well enough tonight to beat a stronger team."
Australia had built a commanding lead through clinical attacking rugby and accurate goal-kicking before the Springboks finally found their rhythm late on. However, by that stage, the deficit proved too large to overcome.
"When you're 25 points behind, there's nobody else to blame but yourself. We rolled the dice a bit, and some guys haven't played a lot together in a long time, but it's not an excuse," he said.
"We picked the team, and we had a game plan, and I thought we had a chance at the end, but the better team won on the night.
"It's sad to lose, but it's not because we've not been together too long. It's because we didn't play well enough."
The result handed the Wallabies a notable scalp and extended their unbeaten run under new coach Les Kiss to six games.
"Australia are a good team and they've definitely improved a lot. They played at home and they're the World Cup hosts next year," he said.
"We might meet them in a vital playoff game, and it was nice to get a taste of them tonight. When we play them next year, we'll know a little bit more about each other.
"I'm not going to say it was a case of lessons learned, but I think it was a valuable experience."