"Real Mallorca will not sit on its hands after the confirmation of this injustice," the Balearic Islands club, who are in administration, said on their website.
The club added they will wait for full details of UEFA's decision, which was published on the European governing body's website on Friday, before lodging a new appeal with CAS.
Switzerland-based CAS is an independent institution which tries to settle sports-related disputes through arbitration or mediation.
Mallorca, part-owned by tennis world number one and island native Rafa Nadal, finished fifth in La Liga last campaign and qualified for the Europa League, the continent's second-tier club competition.
However, financial difficulties had forced them into voluntary administration earlier in the year and UEFA ruled last week they could not take up their place in the competition.
Their licence had not been correctly awarded and the club "did not sufficiently fulfil its financial obligations", UEFA said in a statement on Friday justifying the rejection of the initial appeal.
Mallorca's place in the Europa League has provisionally been taken by Villarreal.
Nadal became a shareholder in the club this month and his uncle, former football professional Miguel Angel Nadal, is new coach Michael Laudrup's assistant.
