Arsenal took the lead in the first half of their game, but conceded twice in 10 second half minutes, prompting Zaha to complain on Twitter.
The 20-year-old wrote: "I swear I'm not watching arsenal anymore."
He then appeared to support the scathing assessment of TV pundit, and former Palace striker, Mark Bright, when he retweeted: "Arsenal are poor. Plain and simple. Sorry @IanWright0 its so annoying watching them, used be made of steel. Now, papier mache!"
Shortly afterwards, he added: "I am a arsenal supporter but they stress me out.."