The FA will launch an investigation into that incident and scenes of crowd disturbances in the away section.
"We strongly condemn any such behaviour and will work with both clubs and the authorities to identify those responsible," the FA said on its website (www.thefa.com).
Reading, 16th in the Championship, hit back with goals from Paul McShane, Michael Hector and Lucas Piazon after visiting Albion, 14th in the Premier League, had taken the lead in the fifth-round tie through captain Darren Fletcher.
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After the final whistle midfielder Brunt, an Albion stalwart, went to hand his shirt to a young supporter and was struck by a coin thrown from the area housing West Brom fans, suffering a cut just underneath his left eye.
Fans then started to scuffle among themselves as stewards intervened.
"Our supporters obviously think it's okay to throw coins at their own players. It's absolutely disgusting," Northern Ireland international Brunt told BBC Sport. "I am ashamed of them today.
"If people come to matches and think it is acceptable to throw coins at footballers or anyone else, it is disgusting.
"If they want to come forward and say they don't like what they've seen then that's fine. Fans are frustrated, we were 1-0 up and lost.
"They paid a lot of money to come, but a small minority spoilt it. There were young kids there. I was absolutely disgusted and ashamed."
West Brom manager Tony Pulis was equally appalled.
"We have seen an incident today where a lad who has played over 300 games for this club could have had his eye out. That is not acceptable. I hope the police get involved, never mind the club. That is criminal," he said.
"People have a drink before the game and you have incidents like this. This is one of the worst things I've seen, a coin thrown at him by one of his own supporters."
(Reporting by Martyn Herman, editing by Ian Chadband)
