World Rugby plans to review the process which saw South Africa named preferred bidder only for France to be chosen to host the 2023 Rugby World Cup.
World Rugby chairman Bill Beaumont 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.
SA Rugby president Mark Alexander said: "This is the first time ever World Rugby has made a recommendation and they voted against it.
"(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, which saw France and Ireland question aspects of the judgement and World Rugby respond 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%" 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 instead 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 of voting 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 which saw even neighbours Scotland and Wales vote against them.
Browne added: "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."
South Africa lost 30-3 to Ireland in Dublin last Saturday and go to Paris to face France this weekend.
Roux added: "I'm still trying to figure out which is the worst result. Last Saturday's or today.
"Maybe the only silver lining is the last time we played there in a World Cup we won it (in 2007). Maybe we'll win it again in 2023."
Laporte added: "We're very happy to host them and we'll host them well. I do understand their disappointment."