After Mohamed Diame scored the opener, Luka Milivojevic levelled proceedings for Palace from the penalty spot.
Roy Hodgson’s men could have won the games had they buried the numerous opportunities that came their way in the second half.
The forward made his 20th league appearance this season in the outing but could do little to help his side nick the maximum points.
And the Coted'Ivoire international has taken to the social media to show his disappointment at the outcome of the encounter.
“Frustrating to not take all three points after a strong second half performance but we’ll keep fighting,” Zaha tweeted.
Crystal Palace are 14th in the log after gathering 27 points from 25 matches and will be hoping return to winning ways when they clash with Everton on February 10.