The Eagles qualified for Europe for the first time after winning the FA Cup last season but were demoted to the Conference League last week due to what the governing body considers a conflict of interest regarding co-owner John Textor - who part-owns Ligue 1 side and fellow Europa League participants Lyon.
UEFA's decision means that Nottingham Forest, who finished seventh in the Premier League last term, will take Palace's place in the continent's second-tier competition but Parish says the club are taking their fight to the Court of Arbitration for Sport (CAS).
The Palace chairman told The Rest is Football podcast: "We are still fighting. There’s an appeal process, so we go to CAS which is the court for arbitration and, you know, we’re very hopeful. We think we’ve got great legal arguments.
"We don’t think this is the right decision by any means. We know unequivocally that John didn’t have decisive influence over the club.
"We know we proved that beyond all reasonable doubt because it’s a fact."
UEFA regulations state that no owner or co-owner can have a controlling interest in more than one team competing in the same European competition in the same season although the London club argue that Textor did not have a prominent enough role for them to breach the rules.
Parish said: "We feel that there are a lot of very genuine mitigating circumstances and more than enough wriggle room to put us in the competition.
"It does look bad. This is the dream right? This is what keeps football alive. This is why everybody goes, because they think one day they might win a cup and they might qualify for Europe.
"These things can be defining moments for a club and completely change the course of history forever.
"Hopefully when we go to CAS we get the right answer.
"We get the written version of (the ruling) with the detail then apparently the appeal is 10 days."