Stander was sent off in the 23rd minute, but Ireland managed to grind out a 26-20 victory against the Springboks in Cape Town on Saturday.
The flanker jumped into Patrick Lambie as the fly-half got a kick away, seeing Ireland reduced to 14 men.
Schmidt was unhappy with the decision and said there was little Stander could do to prevent the collision.
"I thought the red card was very, very harsh to be honest. CJ's got both hands extended, once you're in the air you can't change your trajectory," he said.
"The one thing I would say, I think Pat Lambie's a super player, I certainly hope that Pat's OK. I know CJ and Pat are friends, and that they know each other. CJ was upset that Pat was hurt as much as he was upset that he had to leave the field.
"It's one of those thing that happens. I think, sometimes, when there is an injury like that, the consequence is that a card comes out and that was the result."
Jared Payne and Conor Murray crossed for Ireland's tries as they held on for victory after the latter put them 18-13 ahead.
Schmidt was full of praise for his team and said they should be delighted with their win.
"It's pretty hard to put into words really," he said.
"I thought it was an incredible collective effort. The nine minutes before half-time when we were down to 13 players, to just put them out in the corner, just to scramble and work as hard as the players did to keep them out.
"There was almost a direct repeat at the end of the second half again. To their attacking left hand corner, we managed to scramble across and three for four players turned up to avoid the try being scored.
"For the players, I think they can be incredibly proud of the effort they put in."