Bong was repeatedly jeered during Saturday's goalless draw between the sides at Turf Moor, while home fans also chanted Rodriguez's name throughout.
Speaking a his post-match press conference, Hughton admitted to being disappointed at the behaviour of those in the stands.
"I was incredibly surprised, I must admit. I certainly didn't expect it," he said. "I thought the reaction of the Burnley supporters towards Gaetan was shameful.
"He's an incredibly disciplined and straight individual - as honest a person as you will meet. It's something that happened, it's not nice at all, and of course he's big enough and strong enough to cope with it."
Bong recently stressed that he stands by his racial abuse claim against Rodriguez, despite the FA's verdict.