The FA will receive referee Steve Tanner's report from the match early next week, however that is not expected to contain details of the alleged incident.
Cardiff have told Press Association Sport that the referee advised he had not been aware of any racism.
Players from both sides had to be separated following the final whistle of the 1-1 draw, and trouble reportedly continued in the tunnel.
Bothroyd claimed the problems started after Chopra - who is of Indian descent - was targeted.
The FA would need evidence before taking action, and an FA spokesman said: "We are reliant on being provided with witness statements."
A Cardiff spokesman said: "As a club we utterly condemn any racist comments from anyone but in this particular case the referee tells us he didn't see or hear anything."