A second-half double by Nicolas Pepe has put the Gunners on course for a comfortable victory over the Seagulls.
The result would see Albion finish 16th, two places above the relegation zone, ahead of Burnley, who are behind at Sheffield United.
Some fans have spoken of their frustration on Twitter, with Albion missing out on an opportunity to earn additional prize money with a higher placed finish.
"Shocking," wrote @ELBadgers. "A win with palace losing would be an extra 4m in the bank. Doesn’t seem any interest out there today."
@SamPeters_BHAFC agreed that the players 'have not looked up for it all game'.
@GoodAgood2196 wrote: "I am not happy right now. There is no excuse for this after winning against the champions."
@FlayedEUW said it has been a 'dreadful display', adding: "Should be ashamed of ourselves. Not the end we should be aiming for."
@bhaszn was also unhappy, commenting: "Worst we've played all season."