Rose was targeted by home fans as his side's 1-0 European Championship qualifying win - secured by Connor Wickham's late goal - was overshadowed by ugly and violent scenes at the finish.
The on-loan Sunderland defender was sent off after the final whistle after kicking the ball into a crowd that baited him with monkey chants and gestures, while Serbian players and officials got involved in a subsequent brawl on the field.
"It started when we went out for the warm-up," Rose told Sky Sports News. "I told Wrigs (Steve Wrigley, assistant manager) what was happening and he told me to try and get through it, that it would be dealt with after the game.
"The fans started with monkey chants every time I went near the touchline and in the second half two stones hit me in the head as I went to get the ball for a throw-in.
"After about 50 minutes, my mind wasn't on the game. I was angry. It was so hard to concentrate that I made a few mistakes.
"When we scored, after 90 minutes worth of abuse, I obviously expressed my emotions. The next thing I knew, all the Serbian players surrounded me, started pushing me, and then a brawl broke out.
"The referee then sent me off for kicking the ball but the game had finished by then. The monkey chants started long before I was sent off. It's not right. (Serbia) have to be banned."
Manager Stuart Pearce described the events as "very sad", while the Football Association released a statement soon after the game confirming it had reported "a number" of racist incidents to UEFA.
UEFA fined Serbia £16,000 when England defender Nedum Onuoha was racially abused during a U21 European Championship meeting between the sides in 2007.
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