I definitely really feel for you. It is terrible to have a false allegation made about you, let alone be fired for it. However, understand that CO is an "at will" employment state and an employer can fire you for any reason or for no apparent reason unless the termination is based on age, gender, disability, race, or ethnicity. You should definitely file for unemployment benefits. Perhaps it would be beneficial to sit down with an employment attorney for an initial consultation to see if there are any avenues that you can pursue that I am missing. Best of luck
The information provided in this answer does not create an attorney-client relationship. If you are interested in his legal services, feel free to call Chris at (303) 409-7635 at his law office in the Denver Tech Center. All initial consultations are free of charge.
My colleague is correct. It does not matter if the accusation is false. The employer does not need a reason to fire you. You can be fired for any reason, no reason, a false accusation, or because the employer had a bad breakfast and thought firing you would make him happy.
I am sorry as well, but unless you have a contract or a basis to claim illegal discrimination, the termination is valid and you don't have any claims. Good luck.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
My colleagues are correct that it is doubtful that you would have success in a wrongful termination claim. However, it may be important to determine whether this inaccurate information will be placed in your personnel file and provided to future employers. For these reasons, you may wish to take some action to prevent that and to have the information removed from your file.