The Court of Arbitration in Sport (CAS) has thrown out Palace's appeal against UEFA's decision.
This means that Nottingham Forest's place in the Europa League is now confirmed, and the two Premier League clubs will effectively swap places.
UEFA had blocked Palace from participating in the Europa League due to their multi-club ownership rule with Olympique Lyon.
The rule states that a club cannot have a significant stake in another club, and Palace's owner, John Textor, had held a 43% stake in the club before selling his shares.
Although Textor has since sold his shares and has no ties with the club, UEFA had deemed that the sale came too late for Palace to participate in the Europa League.
The CAS has confirmed that Palace's appeal has been rejected, but has also acknowledged that the club won the Community Shield on Sunday against Liverpool, which may soften the blow.
The CAS statement says that the panel found that John Textor had shares in both Crystal Palace and Olympique Lyon and was a board member with significant influence over both clubs at the time of UEFA's assessment date.
The panel also dismissed Palace's argument that they received unfair treatment compared to Nottingham Forest and Olympique Lyon.