The fourth round 2-2 draw between the Championship sides at Ewood Park saw a delay to the game after an altercation by Etheridge's goal.
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Referee Keith Stroud stopped proceedings to talk to the England-born Philippines international, before restarting play.
Asked about what happened post-match, Blues manager Eustace told the media: "Neil was racially abused, which is bang out of order.
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"There's no room for any racism at all in society let alone football, really disappointing that that's happened, us as a football club don't condone it at all and we're fully behind Neil."
After confirming that it was a fan involved behind the goal, Eustace was asked about referee Stroud's dealing of the situation.
"100 per cent [he dealt with it well]," he said. "It's a very, very, very serious issue, you can't not take it by the scruff of the neck.
"Neil was shook up a little bit after the game and quite rightly so, but the lads got right round him and made sure he's OK.
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"We'll speak to him on the bus and see how he is.
"I think the referee will report it then it will be up to Blackburn as a club to deal with the situation."