And the International Rugby Board has replied to criticism of referee Alain Rolland's sending off of the player.
"Alain Rolland's decision to issue a red card was absolutely correct," said referees manager Paddy O'Brien.
Wales will not appeal against Warburton's punishment.
O'Brien says Warburton's 18th-minute banishment by Irish official Rolland for the challenge on Vincent Clerc was "in keeping with the clear instructions that match officials have received in recent years regarding dangerous tackling".
New Zealander O'Brien added: "Alain is a highly experienced referee and had a clear view of the incident, which enabled him to make an accurate and instant decision.
"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."
The IRB backed up O'Brien with this statement: "A directive was issued to all Unions and Match Officials in 2009 emphasizing the IRB's zero-tolerance stance towards dangerous tackles and reiterating the following instructions for referees:
"The player is lifted and then forced or 'speared' into the ground (red card offence).
"The lifted player is dropped to the ground from a height with no regard to the player's safety (red card offence).
"For all other types of dangerous lifting tackles a yellow card or penalty may be considered sufficient."
Warburton will be free to play again on 7 November, so will be available for the start of the Heineken Cup.
The Welsh Rugby Union will not appeal against the punishment.
Wales face either New Zealand or Australia in the play-off at Eden Park on Friday and Warburton said: "Obviously I'm very disappointed but all my attention and focus now goes towards the players playing on Friday and supporting them the best I can."
Another International Rugby Board statement read: "The IRB memorandum issued on 8 June, 2009 stated that such tackles "must be dealt with severely by referees and those involved in the off-field disciplinary process"."
Warburton, Wales coach Warren Gatland and Welsh legal representative Aaron Lloyd met judicial officer Christopher Quinlan of England, who decided the offence was mid-range on the scale of seriousness, which has an entry point of a six-week ban.
But Quinlan "found that there were no aggravating features and there were compelling on-field and/or off-field mitigating features including the player's admission, outstanding character and disciplinary record and remorse" in imposing the three-week ban.
Welsh Rugby Union group chief executive Roger Lewis said they were disappointed with the decision, but respected the disciplinary process.
Lewis added: "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."
Wales defence coach Shaun Edwards said on Sunday he was "proud" to be associated with Warburton despite his dismissal.
"I have been involved with a lot of good teams in my life in rugby league and rugby union and all I can say is that I am proud to have my name beside Sam Warburton's," said the former Wigan and Great Britain rugby league star.
"With Sam, it was a dominant hit [tackle] as you expect. He was much more powerful than the guy he tackled and he ended up in a position that got him sent off."
Edwards said immediately after the match that it was a "travesty" that France and not Wales would be playing in Sunday's World Cup final, and he said on Sunday that he felt "empty".
"I just think there's a sense of disappointment that a team who have acquitted themselves so well and want to entertain fans and want to play rugby, are not in the sport's premier blue riband event," he added.
"It is very tempting for me to come out with loud statements, but it is more important I keep my dignity in what is quite a trying time.
"You take comfort from the fact that the men you are involved with are an incredibly courageous, incredibly dedicated group who have come to the premier event and acquitted themselves in such a magnificent manner.
"They are everything that is good about the game of rugby."
France defence coach Dave Ellis, who like Edwards made his name in the 13-man code, said: "I think it was a fantastic rugby league tackle. Unfortunately we are not playing rugby league, we are playing rugby union.
"As soon as I saw it I thought it was a sending-off."
Les Bleus head coach Marc Lievremont also reiterated he thought referee Alain Rolland had made the correct decision.
"[People] can talk about injustice but I have seen the footage again and the red card is justified," he added.
"The referee was consistent. I can't help it if their kicker was not as good as ours. I don't know if the best team won but France are in the final."