Palace secured their spot in the Europa League after a surprising FA Cup final victory against Manchester City in May.
However, UEFA, the governing body of European football, determined that Palace must be relegated to the Conference League due to a conflict of interest involving the club's former director John Textor, who also partially owns the French club Lyon .
Textor distanced himself from Palace at the beginning of July, but the ownership issue pertains to the conclusion of last season when the South London team achieved their first European appearance by winning the first major trophy in their history.
According to UEFA's ruling, this would allow Nottingham Forest, who finished seventh in the Premier League, to take Palace's position in the Europa League, yet Parish has indicated his intention to contest the ruling.
"We are still in the fight," Parish stated during the The Rest is Football podcast. "There is an appeal process, so we will approach CAS, the arbitration court, and we are quite optimistic. We believe we have strong legal arguments.
"We are convinced that this decision is not justified. We know for certain that John did not exert decisive influence over the club.
"We have proven this beyond any reasonable doubt because it is a fact."
UEFA regulations state that no owner or co-owner can hold a controlling interest in more than one club competing in the same European competition during the same season.
Throughout this process, Palace has maintained that Textor did not have a sufficiently controlling role for the club to be in violation of the regulations.
However, the deadline for shareholders to divest their interests in a club or otherwise modify their ownership structure to comply with the regulations was March 1st.