Hello and thank you for entrusting me to assist you. My name is ***** ***** I will do everything I can to answer your question.
I am extremely sorry to hear that you were let go and agree that the circumstances were unfair. Unfortunately, however, employment in the state of TN is "at will" absent an express agreement to the contrary. At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even TRUE.
Thus, there is nothing illegal about being terminated based on the false belief that you made an inappropriate statement. You might be able to sue the employees who falsely claims that you made this statement, but that would be a lawsuit against those individuals in their personal capacity, it would not be a lawsuit against your employer. The problem with such lawsuit would be proof, though. It would essentially be "word against word," and they are two people and you are only one. You have the burden of proof as the plaintiff. This is not the recipe for a strong lawsuit. Given that lawsuits cost a lot of time and money to pursue, it probably would be unwise to pursue a lawsuit on this basis. Not to mention that even if you obtained a judgment you would then have to collect it, and these individuals may very well be incapable of paying any significant sum in damages.
Thus, from a practical and legal standpoint, I'm afraid to say that it's unlikely there is much that can be done under these circumstances. It is highly unfortunate, but most likely your sole recourse is going to be applying for unemployment benefits and seeking new work.
I hope that you find this information helpful and am genuinely sorry if it is not what you were hoping to hear. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.