The islanders have been denied entry to European competition this season for financial irregularities, but are asking UEFA to overturn that decision, claiming many clubs across the continent have similar or even larger debts.
In the match against Feyenoord, which Mallorca won 1-0, the players took to the field with the slogan "UEFA FAIR PLAY PLEASE" on their shirts.
Mallorca have the support of political parties on the island and on the mainland in their bid to be reinstated to the Europa League, a competition for which they qualified after finishing fifth in the Primera Division last season.
Goalkeeper Dudu Aouate hopes UEFA will reconsider their decision.
"Not playing in Europe would be a real shame for the players, the fans and the city," he told the club's website.
Meanwhile, coach Michael Laudrup believes UEFA president Michel Platini did not ratify the decision to ban Mallorca.
"I'm optimistic - I know Platini and I know he's fair," he said in the build-up to the match against Feyenoord.
"The committee (of control and discipline) took the decision, but we'll see what happens. There has been no final word."
Midfielder Pep Lluis Marti is in agreement with his coach.
"I'm sure Platini doesn't support this, because someone like him, who was a footballer himself, knows exactly what it is for a footballer to play in Europe," he told IB3TV.
As things stand, Villarreal will replace Mallorca in Europe next season.