Skipper Jean de Villiers and coach Heyneke Meyer pointed to errors in their 28-8 win over the Wallabies, a record defeat of Australia in Cape Town, as having cost them what could be a vital bonus point.
Having scored two tries in the opening 15 minutes, the Springboks managed just one more in the remainder of the game as their intensity dropped in the second half.
"If you had given us a 20-point win over Australia at the beginning of this year, we would have grabbed it," De Villiers told reporters.
"To beat a very good Australian side by that margin is a great achievement, but having given ourselves 40 minutes to score two tries in the second half, there is some disappointment that we did not manage it.
"For us today the challenge was not the scoreboard, but how we played and we are still not happy with areas of our game."
Meyer echoed those sentiments and knows that the failure to get a bonus point means they now must score four tries against New Zealand at Ellis Park on Saturday and win by more than seven points if they are to claim the Rugby Championship.
After the early onslaught, South Africa had chances deep in Australian territory but were let down by poor handling and passing.
"It is a sign of a great team that you win like this and are not that happy about it," Meyer said. "We decided to move the ball more today and I thought we played some great rugby. But after the game the players weren't happy.
"I want to see a lot of improvement against the All Blacks. We want to be the best team in the world and win the World Cup and to do that we must improve game-by-game."
De Villiers said the New Zealand clash would be another welcome opportunity to test where they were as a side.
"They are the best team in the world and we are looking forward to the game, we want to test ourselves against the best," he added.
"It is at Ellis Park, a lot has happened at that stadium in the past... we just want to come off the field knowing we have given our best."