Warburton was red carded for his dangerous challenge on French wing Vincent Clerc and will now miss the third-place play-off against Australia on Friday.
Referee Alain Rolland's decision to give Warburton his marching orders after just 18 minutes has divided opinion in the rugby world but IRB referees manager Paddy O'Brien is adamant the Irish official made the right call.
He said: "Alain Rolland's decision to issue a red card was absolutely correct," he said.
"It was in keeping with the clear instructions that match officials have received in recent years regarding dangerous tackling.
"Alain is a highly experienced referee and had a clear view of the incident, which enabled him to make an accurate and instant decision.
"The lifted player is dropped to the ground from a height with no regard to the player's safety.
"Player welfare is paramount and Unions, teams and match officials are all aware of the responsibility to eradicate dangerous play.
"This message was reiterated as recently as the week before Rugby World Cup 2011 kicked off when we hosted briefings at a workshop with match officials and coaches."
Following the hearing, WRU chief executive Roger Lewis revealed the union want to draw a line under the matter.
He said:"We are disappointed with the decision to suspend Wales captain Sam Warburton from the game for three weeks, following his red card dismissal in the Rugby World Cup semi-final.
"The WRU respects the process which has been followed and understands the disciplinary procedures in place.
"Our focus in now totally upon the forthcoming third place play-off international, which will be played at Eden Park in Auckland on Friday.
"The WRU further wishes to state its unequivocal support for Sam Warburton as a role model and exemplary captain who has led Wales to formidable success in the competition so far."