The West Bromwich Albion forward was accused of using "abusive and/or insulting words which included a reference to ethnic origin and/or colour and/or race" towards Bong during the Baggies' 2-0 win over the Seagulls on January 13.
Last week, the Football Association announced that an Independent Regulatory Commission "determined that on the balance of probabilities the allegation was not proven" against Rodriguez.
On Wednesday, Brighton issued a statement on behalf of their player, who remains insistent that he did not mishear what Rodriguez said to him during the game.
The statement read: "Mr Rodriguez's actions during our game against West Bromwich Albion, followed by statements issued by him and on his behalf by his various PR and legal advisors, have resulted in my character being questioned and subsequently for a number of accusations to be directed at me.
"Please let me be clear: I know what I heard and I did not mishear. My conscience in raising the complaint is therefore entirely clear.
"This was my first such experience in more than three years in this country and I would never seek to bring a false charge against a fellow professional.
"Those who have accused me of doing that do not know me. Equally those who have expressed an opinion were not there on the pitch at the time and only Mr Rodriguez and I know exactly what was said and I stand by my original complaint.
"I now wish to continue with my career, and won't be commenting further on this matter even if Mr Rodriguez chooses to issue any further statements."
The statement concluded by clarifying that the club "fully support" their player in his stance, and will similarly not be commenting any further.