Sections of the home crowd jeered the Cameroon international at Turf Moor and sung songs of support for former Clarets player Jay Rodriguez, who was alleged by Bong to have made a racist remark during a match between Brighton and West Brom in January.
Seagulls boss Chris Hughton described the booing as "shameful" and his view was supported by the FA, which deemed it "unacceptable".
"It needs repeating, following the recent disciplinary matter, that there was no suggestion by any party involved in that case that the player made a malicious or fabricated complaint," an FA statement read.
"The FA was wholly satisfied that the complaint was made in absolute good faith.
"The FA takes all allegations of discrimination extremely seriously and continues to encourage all participants who believe that they have been the subject of or witness to discriminatory abuse to report this through the appropriate channels."
Hughton, speaking in his post-match news conference on Saturday, made no secret of his displeasure for the Burnley fans' behaviour.
"I thought the reaction of the Burnley supporters to Gaetan every time he got the ball was shameful," he said.
"What they should do is look at the two statements - one from the independent committee, one from the FA.
"I was incredibly surprised [by the boos], I certainly didn't expect it here."