Chopra, whose father is Indian, was invited to a reception at Buckingham Palace for sports and entertainment stars with Indian connections earlier this week.
Players from both sides had to be separated after a melee ensued following the final whistle of the 1-1 draw and the trouble reportedly continued in the tunnel after the game.
Bothroyd claimed the problems started after Chopra - who is of Indian descent - was racially abused and told Wales Online: "I wasn't there but I spoke to Chops and he said one of their boys made a racist comment to him.
"That is obviously not acceptable in this game and it's something I think the referee might have to deal with.
"We were wearing T-shirts today that said 'Kick Racism Out Of Football' and then something like that happens.
"It's not a good example to set for football in general.
"If you call someone a racist name people are going to react and that's happened at the end."