Rugby Australia today confirmed that the Code of Conduct matter had been formally concluded, with Folau failing to meet the 72-hour deadline to appeal the decision.
However, Folau said his decision not to appeal the verdict was not an acceptance of the findings of the three-person independent panel, which had found him guilty of a high-level Code of Conduct breach.
"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.
"I will not be exercising my right to appeal Rugby Australia's decision to terminate my employment contract.
"My decision not to commence Rugby Australia's appeal process is in no way an acceptance of the judicial panel's findings.
"I simply do not have confidence in Rugby Australia's ability to treat me fairly or lawfully throughout this process."
The 30-year-old said he wanted to continue playing rugby and is considering all options.
The Daily Telegraph has reported that the most likely option could see Folau take Rugby Australia to the Supreme Court.
"The messages of support from fans, players, former rugby administrators and the public have been humbling," Folau said.
"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.
"Ultimately, I need to do what is best for my family, my teammates and the fans, so I am considering all potential avenues open to me."
There had been reports that Folau taking Rugby Australia to court would significantly impact on the organisation's finances, but CEO Raelene Castle said a loss in a court appeal wouldn't end Rugby Australia.
"I think it is an exaggeration to say it will imperil the game's finances — I don't believe that to be true," she said.
"Certainly I believe this is money that we could be spending on the rugby community and that's disappointing. Every dollar that we spend on legal fees is a dollar that we don't spend in the community.
"What I would say is that Israel also knew the implications. The first time around when he posted the first time and the implications for the wider game was something the tribunal took into consideration, both financial and also reputation from a disrepute perspective, when they got to the stage where they decided termination was the only option."
