Television footage of the second-half incident showed the pair arguing and colliding with each other.
Rodriguez then held his nose and waved his hand at Bong, as if to suggest the Cameroon player had given off a bad smell, although it was not clear what was said.
An annoyed Bong immediately complained to referee Martin Atkinson who noted the complaint in his match report.
Following the match, Bong tweeted: "Some words should not be said on a football field and specially not by players Rodriguez words are unforgivable for the man I am!!"
England's governing Football Association confirmed on Sunday that it had launched an investigation and on Monday Brighton chief executive Paul Barber give the south coast club's backing to Bong.
"Gaetan has the full support of everyone at the club through this process," said Barber. "The club will also assist the Football Association in their investigation, but at this stage we would prefer not to make any further comment until this process has concluded."
Brighton manager Chris Hughton, speaking to reporters after the game, said he was aware of the allegation but added it was dealt with "in the correct manner".
West Brom boss Alan Pardew said he had not seen the incident but found it "very difficult" to believe that Rodriguez, an England international, would make a racist comment.
"Jay Rodriguez claims that the allegation, whatever the allegation is, is untrue," Pardew insisted.
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