Palace, this season's FA Cup winner,will instead compete in the Europa Conference League due to UEFA's multi-club rule, with Olympique Lyon holding their place in the Europa League.
John Textor retains his shareholding in Palace and also is owner of Lyon, which runs against UEFA's multi-club rules.
"We're devastated," Parish told Sky Sports. "It's a bad day for football. It's a terrible injustice. I do believe nobody want to see this. I don't think Uefa wants to see this.
"We've been locked out of a European competition on the most ridiculous technicality. Supporters of all clubs should be devastated for us."
We have nothing to do with Lyon
Parish also fumed: "Everyone knows we're not part of a multi-club set-up.
"We don't share any staff. We're caught up in a rule that wasn't put there for us. I don't understand why the panel has come to the conclusion they have done. I think we've shown John had no influence over our club.
"This is a ludicrous decision. We will ask the appeal court to listen to our argument."
Textor has agreed to sell his 43 per cent stake in Palace to Woody Johnson, but the deal is yet to be settled.