Chopra, who is half Indian, alleged Palace captain Shaun Derry had called him a racist name and had to be dragged away from Derry after the row triggered ugly scenes at the final whistle.
But Palace firmly rejected the claims and said they "would welcome any FA enquiry into racist comments allegedly made by one of our players".
The statement continued: "Crystal Palace are a multi ethnic club and are proud of its history in this respect. We take great exception at the outrageous allegations being levelled at us by Cardiff City players and management.
"We would like to make it known that we are 100 per cent supportive in this matter of all of our players and definitive in our belief that none of them would make any racist comments.
"As a club we are fully behind the Kick Racism Out of Football campaign, as are all of our players."