Angry Hammers fans condemned the winger on social media after video footage emerged of him appearing to spit in Rice's direction after the ball runs out of play.
It prompted a response from Zaha on his Instagram account on Sunday morning denying that he did anything wrong.
Lying in bed as he filmed the clip, Zaha said: "Let me clear up something that the West Ham fans are trying to make up.
"On your own video, you can see that Declan runs in front of me and I spit to the right.
"So please don't make up lies that I spat at someone. I have never done it and I never will.
"So please, let's just accept that we won the game and move on."