The statement followed a major,if temporary,victory for RA and NSW Rugby on the matter,with the panel finding Folau's conduct constituted a"high-level breach"and warranted his sacking.
Folau has the right to appeal the decision,characterised as"landmark"by Castle,and has 72 hours to do so through the game's code of conduct process.
He could also seek a court injunction to stop RA from terminating his contract,then seek to have his case heard in either the NSW Supreme Court or the Federal Court.
Castle said RA would deal with that situation as it came.
"This is a decision that will change the landscape of sport across Australia and perhaps internationally,"she said.
"The tribunal were the best possible experts in their field that we could put together and they have spent a lot of time to ensure that they get this right. It will be landmark and it is important and it is a big decision.
"Israel is a very important player in our game,he has been over a long period of time,and we wanted to make sure we took the time to get it right."
As it stands,the decision is set to bring to an end Folau's six-year partnership with the Waratahs and Wallabies,a union that was unexpected at the time but that went on to be a huge success. He was a key part of the Waratahs'2014 Super Rugby title win and only this season became the all-time top try scorer in Super Rugby history.
Notwithstanding his right of appeal,it also effectively signals the end of Folau's professional sporting career in Australia,after the Australian Rugby League Commission indicated the former Kangaroo would not be welcomed back to the NRL.
He could potentially be picked up by a club in Japan's cash-rich Top League,but European rugby seems less likely given the heavy criticism he endured from UK and Irish pundits last year and the recent controversy over Billy Vunipola's support for Folau.
"We want to stress that this outcome is a painful situation for the game,"Castle said.
"Rugby Australia did not choose to be in this situation,but Rugby Australia’s position remains that Israel,through his actions,left us with no choice but to pursue the course of action resulting in today's outcome.
"This has been an extremely challenging period for rugby and this issue has created an unwanted distraction in an important year for the sport and for the Wallabies team.
"But our clear message to all rugby fans today is that we need to stand by our values and the qualities of inclusion,passion,integrity,discipline,respect and teamwork.
"When we say rugby is a game for all,we mean it. People need to feel safe and welcomed in our game regardless of their gender,race,background,religion,or sexuality."
After making his Test debut on the wing in the Wallabies'2013 series against the British and Irish Lions,Folau became a permanent fixture in the Australian back line under Robbie Deans,Ewen McKenzie and then Michael Cheika. He scored 37 tries across his 73 Tests and was awarded the John Eales Medal three times by his peers.
The Wallabies'major sponsor Qantas,which campaigned in favour of same-sex marriage,said:"As a sponsor,we think it’s important that Rugby Australia has sent a clear message that singling out vulnerable LGBTI people under any circumstances is out of step with their values,not to mention the values of the community at large."