As a number of respondents have said, it really depends on your university's policies on supervision, vivas and appeals, but it is likely that there are three issues here.
The question of adequate supervision. Were you supervised properly in essence? Was your supervisor reasonable in approving your submission or did they guide you correctly in your choice of topic etc? Very often that will come down to the documentary trail on meetings, discussions on the parts that led to the fail etc.
The conduct of the viva. Was it procedurally correct? It is highly unlikely that you can appeal on the grounds of the examiners' academic judgement.
Which leads to the quality of your work. Is it of sufficient quality for you to be awarded with a doctorate?
It might be that you could establish a procedural irregularity in the exam or that you were subject to inadequate supervision but that still leaves open the question of the quality of your completed work. In other words, it might be that you deserve some kind of remedy, but that remedy might not entail you being awarded with a PhD.
Your first step is likely to engage with the relevant officers in your students' union, if they exist, and also to have a conversation with your Head of School about possible next steps. That second conversation might be best managed towards discovering what your department's attitude is, not for you to rehearse your own feelings on the matter.