World Rugby plans to review the process in which South Africa had been named preferred bidder, only for France to be chosen to host the 2023 Rugby World Cup.
World Rugby chairman Bill Beaumont has denied being humiliated as the membership voted against the recommendation by the governing body's independent evaluation committee.
Beaumont, who repeatedly defended the bidding process as open and transparent, said: "A humiliation for me? I don't think so.
"We've made a recommendation. The recommendation wasn't accepted by council.
"Just because it went to France doesn't mean there's humiliation whatsoever.
"We will learn as we move forwards. This is the first time we've embarked on this process."
South Africa Rugby described the two weeks since it was named preferred candidate as entirely opaque and hit out at rivals France and Ireland for not complying with a code of conduct.
"This is the first time ever World Rugby has made a recommendation and they voted against it," SA Rugby president Mark Alexander said.
"(But) a set of rules was broken during that process which we are upset about."
Alexander was referring to the fallout from the publication of the independent recommendation, in which France and Ireland questioned aspects of the judgment and World Rugby responded to those allegations.
French bid chief Bernard Laporte felt the communication over a "misunderstanding" within the independent report "helped us - maybe".
South Africa felt 99 per cent certain it would be hosting the tournament for a second time, after its successful staging in 1995 when the Springboks won in the first tournament in the post-Apartheid era.
But, South Africa missed out for a fourth-successive time.
A simple majority from the 39 votes was required and France claimed 24 in the second round to be selected as hosts of the 10th edition, ahead of South Africa, after Ireland's elimination in round one.
Chief executive Jurie Roux insisted South Africa would take the experience on the chin and it would not put them off making a future bid.
"If it depends on me, absolutely... we'll try again. At some stage, we need to bring it back - hopefully 2027," Roux added.
"You can't win it if you're not in it. It's like the lottery, although it feels like a lottery. My ticket had the wrong numbers."
Irish Rugby Football Union chief executive Philip Browne was magnanimous in a defeat during which even neighbours Scotland and Wales voted against them.
"If we had any difficulty, the difficulty was with the evaluation report, where we felt it was lacking in certain areas.
"I don't think we could've done anything more than we did."