The 11-time champions crashed out of the play-offs for a second consecutive year with Pool A defeats to Fiji and Argentina in the HSBC SVNS opener on Saturday.
The Blitzboks started well by defeating France 15-12 in their opening match, but successive defeats to Fiji (28-10) and Argentina (19-14) eliminated them from play-off contention.
They will now play Great Britain in the fifth-place semi-final, with much reflection needed overnight to deliver a more streamlined performance on Sunday.
Pool A proved close, with France, South Africa, Fiji and Argentina all managing wins. But only the Blitzboks fully understood the equation: they needed to beat the Pumas by 35 to reach the semi-finals.
Trailing 12-0 at half-time made that mission almost impossible. Although South Africa hit back with two second-half tries to edge ahead, their defence - shaky all day - let them down again late on.
The day had started well with a gritty win over France. The Blitzboks scored three tries to two, with two moments of Selvyn Davids brilliance proving decisive.
After France dominated the early exchanges, a turnover allowed Ryan Oosthuizen to race 70 metres for the opener. France hit back for 7-5, before Donavan Don reclaimed the lead by gathering a wicked Davids kick.
Christie Grobbelaar's try, again created by a sublime delayed pass from Davids, stretched the lead to 15-7, with a late France try not enough to change the result.
Against Fiji, the Blitzboks started brightly again, Ronald Brown sniping through for 5-0. But from there the wheels came off.
A missed tackle from Don handed Fiji momentum, and another defensive lapse pushed the islanders into a 14-5 half-time lead.
The second half was more of the same: Fiji dominated the breakdown, pushed the physical limits - without consequence from referee George Selwood - and tore SA apart with sharp attacking touches, racing to 28-5. Tristan Leyds grabbed a late consolation, but the result was long settled.