The Boks found themselves 14 points behind at the break after France capitalised on their opportunities.
South Africa responded strongly in the second half, putting the hosts under sustained pressure, but their comeback ultimately fell short.
Erasmus says the Springboks created opportunities to change the outcome, but their execution in key moments let them down.
"We were a little bit off, it's one point here, one point there and tonight they took their opportunities when they got it and we didn't. It's an old cliché, I definitely think we had enough opportunities, two simple tries, we could have scored with one last pass and then maybe one or two wrong decisions,” Erasmus said.
“Maybe a corner rather than expecting the referee to give four penalties in a row in front of a crowd like this to keep penalising the home team."
South Africa showed greater urgency after half-time but captain Siya Kolisi admits the Springboks have themselves to blame for not taking their chances, while acknowledging the quality of the French performance.
"They played really well tonight and I think as coach said I think especially in the first half early, we created some opportunities that we didn't take in the wide channels. When they created opportunities they took them straight away and we could have been better in the first part,” Kolisi added.
“The effort and hard work was there from them too, they played well, they fought to the end but if you create so many opportunities and don't take as many with a team like this, you're not gonna get the win and we know what we need to fix and hopefully we'll be better next week."