The Springboks clinched a 24-13 victory after delivering a dominant performance in which the home side were given four yellow cards and one red.
Ryan was red-carded midway through the first half after making contact with the head of Bok hooker Malcolm Marx with a diving cleanout deep inside South Africa's 22.
His second-row partner Tadhg Beirne crossed the whitewash shortly afterwards, but that effort was ruled out after referee Matthew Carley saw Ryan's indiscretion on television replays and sent him to the bin.
Carley initially issued a yellow card to the 29-year-old but that was upgraded to red by the Foul Play Review Officer which meant Ireland played most of the remainder of the match with 14 men.
Ryan has admitted that he felt bad for letting his team down in that encounter.
"I was devastated, to be honest. Because it was at such an important point in the game. We'd just scored, the try got reversed. They got a penalty and I was sent off," he said.
"Big moment in the game and I felt like I let the lads down a little bit there really.
"The big thing now for me is just making sure I learn from it and it doesn't happen again. Because at that level, it's such fine margins and it probably cost us a little bit in the end.
"I'm not going to make any excuses for it. We want to play on the edge, but you can't obviously tuck your shoulder or go off feet like that.
"To be honest, it was just a poor moment for me more than anything.
"It would be easy to say, we play on the edge and these things happen. Hitting rucks for a second row forward is one of your primary roles.
"So, I just need to do better there really."
Ryan subsequently appeared before an independent disciplinary committee, who deemed his actions to be mid-range, providing the starting point of a six-week suspension, but full mitigation was applied given the player's admittance of guilt and his clean record.
That meant he was handed a three-week ban but the lock completed World Rugby's Coaching Intervention Programme, which is commonly referred to as the "tackle school" and, by doing that, he only missed Leinster's URC clash against the Dragons and their Investec Champions Cup opener with Harlequins.
Ryan's participation in the "tackle school" meant he returned to action in Leinster's narrow Champions Cup win over Leicester last weekend and he gave some insight into what the programme entails.
"It was just some scenario stuff, so we'd kind of mimic maybe the ruck again. We'd put a couple of tackle pads into the back of the ruck to lengthen it a little bit," he said.
"I talked through maybe what I should have done differently and what I will do next time. We'd record that and send it on to them. I think I ticked off every box and they were happy with it."