The England international was given a hostile reception from the travelling faithful at Selhurst Park, having recently agreed to join Leeds's rivals Manchester United in the summer.
Having heard the taunts, 20-year-old Zaha aimed his middle figures towards the Leeds fans - an act that he now regrets.
"On that note I also wanted to apologise for the gesture I did towards the Leeds fans in yesterday's game. Very unprofessional from me," he wrote on Twitter.
United are believed to have parted with around £12m to sign Zaha.