Exiles full-back Ben Loader was dismissed after just 18 minutes for a dangerous tackle on Springboks fly-half Manie Libbok.
Replacement prop Ciaran Parker, on the pitch for barely a minute, was then sent off for an illegal clear-out.
Stormers coach John Dobson said Libbok would be out for "a little while" after suffering a significant head injury.
"There's no way Ben Loader comes in there trying to decapitate Manie. It's one hell of a tough situation - play was moving fast, it was a two on one, there was a try at risk," said Dobson after a bonus-point win kept the South Africans in contention for a last 16 spot.
"You want to see if you can make a hit and move across. But it's a red card. We don't view it as any form of malice, but it's also not great when your Springbok fly-half is out of the game with an HIA.
"I would differentiate slightly between Ben Loader's tackle which was a high-speed rugby action when Deon Fourie got hit as a jackler - that's where you've got to protect because guys are really exposed."
French referee Ludovic Cayre also handed out three yellow cards and awarded two penalty tries in the match.
Edinburgh moved to the verge of qualification with a bonus-point 34-21 win at Castres which eliminated the French side.
Hooker Dave Cherry, No. 8 Bill Mata, centre Cameron Hutchison and scrum-half Ben Vellacott scored tries for the Scots.
"We played for 50 minutes, but we forgot about the last 30 minutes," complained Castres prop Quentin Walcker.
Racing 92 stayed on course for the next stage with a nervy 30-29 win over Harlequins.
Victory was secured by a 77th-minute penalty from Nolann Le Garrec and came despite Racing having just 12 players on the field after a flurry of late yellow cards.
"I can't be happy with this match, even if we won. We should have killed the game and we didn't," said Racing centre and skipper Gael Fickou.
Racing will face a tough challenge in order to secure qualification next weekend when they travel to Dublin to face four-time champions Leinster.
