The exam you took has been optimized for selection only. You are not informed what exactly went wrong during the exam, how much does it went wrong, was it "lights out" or just a narrow miss. This approach kills in place all unfair attempts to complain but also does not help beyond the process of selection.
An exam that appears easy ("just perform any three pieces of your choice, no restrictions") may actually be very difficult, depending on how are these pieces envisioned by commission. While you have not seen obvious written rules, it may be some unwritten rules about these pieces, or other behavior like attempt to self-accompany with piano while singing. The commission may declare they are "ready for everything" yet do not like unusual approaches if other good applicants present something more expected.
There are exams that are optimized to certify the standard grade rather than to select into some group matching requirements of the unknown difficulty. Take ABRSM grade exam or similar. It should give you more feedback.