Folau, who was set to be a key part of the Wallabies plans at the World Cup this year, has not played since posting a banner on Instagram last month that read: "Drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolators - Hell awaits you".
Reports in Australia last week suggested that Folau was always planning to skip the appeals process after he was found guilty of a high-level breach of the ruling body's code of conduct.
Folau added that he was considering his options "in the face of growing discontent" with the way Rugby Australia had handled his initial code of conduct hearing.
"The last few weeks and, in particular, the last 72 hours have given me considerable opportunity to reflect and think about my future", Folau said.
Israel Folau failed to appeal his sacking over homophobic comments within a 72-hour deadline, Rugby Australia said on Monday.
"I believe I still have a lot of rugby left in me and the potential impact of Rugby Australia's decision on my reputation and my career is substantial".
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While it remains open to Mr Folau to appeal this finding to a different panel, it has been reported that Mr Folau intends to instead pursue the matter in the Supreme Court of NSW, as he believes he has been persecuted on the basis of his religious beliefs.
Israel Folau, who calls himself a devout Christian, has argued that his contentious social media post contained a passage from the bible.
That came after Folau had been warned against making such posts before signing his new contract previous year.
"The messages of support from fans, players, former rugby administrators and the public have been humbling", Folau continued.
Rugby Australia chief Raelene Castle has said there were no winners from the row and admitted regret to not foreseeing further potential problems after he was let off previous year.
Rugby Australia CEO Raelene Castle said at the time the decision would have ramifications across the sporting world.
In addition to his rugby union career, Folau has also played professional rugby league and Australian rules football.