Pictures show Zaha spitting at the same time as the West Ham midfielder runs past him, prompting some supporters to claim that the winger was intentionally spitting at Rice.
Taking to Instagram on the morning after the game, 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.
"Because I've never done it and I never will, so please, let's just accept that we won the game and move on. To be totally honest, normally I wouldn't even care about things like this. But making up lies, that's not it, you can dislike me, you can feel however you feel about me, just don't make up nonsense."
Zaha, who came through Palace's academy, has made 332 appearances for the Eagles in all competitions, scoring 53 times.