The Northern Ireland international had gone over to applaud the visiting fans following their FA Cup fifth-round exit, but went down clutching his face as he approached the away end.
Brunt, who suffered a cut under his left eye, said a coin had been thrown at him by the fans, while boss Tony Pulis claimed the player could have been blinded.
"I've still got the 50p," Brunt said. "I spotted a little girl in the front row and wanted to give her my shirt.
"Obviously there's some people in the front who were angry, understandably, because we didn't play well or get the result we wanted.
"But there's absolutely no excuse for that and no place for it in football. I've been here a long time. Obviously we all get our fair share of stick but to be hit with a coin by your own fans is absolutely disgusting.
"The guy who threw it knows who he is and knows all this week where I'll be, and next Saturday if he wants to come and have a word about it that's not a problem - I'll meet him wherever he wants.
"I've been here a long time and I've loved my time here and that's the first time I've been ashamed of our supporters. A small minority obviously ruined it for the rest of the 4,000 who were there and paid good money for a day trip."
The FA will look into the incident, as well as the crowd disturbances in the Baggies' end of the Madejski Stadium.
A statement from the FA on Saturday evening read: "The FA is investigating the incident in which an object was thrown from the crowd at Chris Brunt at the end of the Reading v West Bromwich Albion game on Saturday (20 February 2016) as well as the crowd disturbances in the away section of the stadium.
"We strongly condemn any such behaviour and will work with both clubs and the authorities to identify those responsible."
A Thames Valley Police spokesperson said: "The incident will be dealt with as an assault and we will be working with West Bromwich Albion and Reading to resolve the issue and identify anyone involved."
Pulis said: "We have seen an incident where a lad who has played over 300 games for this club could have had his eye out.
"He has a cut and it's not too far away from his eye - it's an inch away from striking him in his eye and if that happens we're talking (about) a very, very serious problem.
"It's barbaric. That's not acceptable. West Bromwich Albion is a fantastic football club, a famous club, but you can't condone that.
"I think the police have to get involved in this. I don't think you can allow that to go by. That's criminal, and I mean criminal.
"This has got to be one of the worst things I have seen, for Chris to have a coin thrown at him from his own supporters having been at the club for such a long time. Every decent supporter of the club will be absolutely devastated it has happened to their football club.
"It's the way the game is going. Social media and everything else builds up an anti-feeling if things are not going well at football clubs. We have to be very careful with it."
Brunt, 31, did hand his shirt over to a supporter after gesturing and remonstrating with another group who had made their way to the front of the stand as he moved closer to apologise for Albion's exit.
Reading boss Brian McDermott added: "It's outrageous, stuff like that, it's not right and proper. We will co-operate with whatever we have to and make sure we find the person who threw it."
Goals from Paul McShane, Michael Hector and Lucas Piazon sent Reading through to the FA Cup quarter-finals for just the fifth time in their history. Darren Fletcher's opener for West Brom was eventually worthless.
Albion have won just twice in the last 11 games, with Pulis under pressure from a section of supporters. The Baggies are 14th in the Barclays Premier League, eight points above the relegation zone.
It is understood the fan who allegedly threw the coin has been identified by stewards in a picture which has now been passed to police and West Brom will issue a lifetime ban if they are found guilty.
A club spokesman said: "The offender can expect the severest possible sanctions."