"We're not at their level yet," Saint-Andre said. "I must congratulate my players for the commitment they showed out there, but you can't start against one of the best teams in the world by giving them seven points. We're not too far away but if we're the fifth best nation in the world then we're in our rightful place. We're still missing that little bit extra."
Left winger Yoann Huget's try just before halftime gave the French hope after they trailed 13-0.
"Our team really has a good future but after every game we realize that there is another layer to add," France captain Thierry Dusautoir said.
The Springboks never looked like being overtaken and had two tries ruled out for knockons. They defended high up the field, tackling with ferocity and Morne Steyn made it 10-0 with a kick from some 40 meters out wide on the left.
"I must be honest. Even at the toss with Thierry you could feel that they were a little bit nervous," South Africa captain Jean de Villiers said. "We got a bit of motivation from that and we knew that if we started well we could get the upper hand."
De Villiers praised his players for the level of consistency they've shown.
"We're very happy with the last 12 months. If you take the end of last year into account it's 13 wins from 15," he said. "Results wise, that's one of the best years South Africa rugby's had for some time."
Although France's tackling was tighter than it was in last Saturday's 38-18 win against Tonga there was little flair.
"They are an exceptionally efficient side, while sometimes we make things too difficult for ourselves," Saint-Andre said.
No. 8 Damien Chouly went on a decent surging run but that move ended with a poor offload, something which has dogged France of late. That was highlighted when Wesley Fofana tried an ambitious pass that his midfield counterpart De Villiers intercepted, but the Springboks captain could not hold onto the ball with the field clear.
Steyn slotted over again before the break but moments later a rare lapse in concentration saw lock Pascal Pape and Parra combine to set Huget free, and he just beat Pietersen and Steyn in the left corner. The try was given after a long video replay and Parra converted from the left as South Africa went into the dressing room 13-7 up.
If that try gave the French hope, they were soon on the back foot in the second half.
De Villiers picked up the loose ball after Steyn dropped scrumhalf Ruan Pienaar's pass and broke some weak tackles before offloading to give Fourie an easy score. But, following a video replay, the try was ruled out for a knockon.
The video was used again in the 51st when Huget flung himself to try and get to the ball before Francois Louw as he chased down Steyn's chipped pass, and again a knockon was the verdict.
Steyn proved unflinchingly accurate with the boot and landed another long-range effort to make it 16-7.
Huget went close to his second try when he chased down his own kick ahead, but the bounce went against him.