Roy Hodgson’s men came from behind to secure a second successive Premier League win thanks to goals from Patrick van Aanholt and Jordan Ayew at the London Stadium.
And Hammers fans were furious after footage on social media appeared to show Zaha spitting in the direction of Rice.
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But Zaha has denied the accusations on his Instagram Story, in clips which have since been deleted.
He said: “Let me clear 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.