"I think we basically killed our dreams for the Nations Championship tonight with this performance and not getting the win and the four tries," Erasmus told a press conference.
South Africa, who suffered their first defeat of the Nations Championship, remain top of the Southern Hemisphere table on 21 points, but New Zealand are one point behind with a game in hand.
The Springboks will visit Ireland next week to conclude the group phase, while the All Blacks play Wales on Saturday before facing England the following Saturday.
Erasmus lamented his side's lack of discipline, as they conceded 11 penalties, eight of them in their own half. Lood de Jager was shown a yellow card for a high tackle, while Jasper Wiese was sent off for 20 minutes after the bunker upgraded his yellow card for a head-high hit.
"It hurt us. That caused us in a big way. I don't think any of that was intentional, but I agree that it should have been cards," Erasmus said.
"I guess the frustration is that the discipline cost us."
France also received three yellow cards through scrumhalf Maxime Lucu, winger Aaron Grandidier-Nkanang and tighthead prop Regis Montagne.
Erasmus was far from satisfied with the performance. It was also South Africa's first defeat against Les Bleus at the Stade de France since 2005.
"We didn't play well, so don’t find a lot of excuses," Erasmus said. "I don't think there's much more to blame than ourselves."
Nations Championship 2026
The inaugural Nations Championship will see six northern hemisphere and six southern hemisphere nations battle it out across six rounds in the July and November international windows before assembling in Twickenham for one unforgettable finals weekend on November 27-29.
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