In an at-will employment situation, you can be fired for any or no reason (baring circumstances you didn't mention here).
FYI, in many states you cannot collect unemployment if you were fired for cause.
You best option may be to put it behind you and move on if you believe the employer is not interested in anything more you have to say.
See a NC employment attorney ASAP.
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In NC you can be fired for any reason or no reason at all (except for discrimination). If you were fired for using drugs in the kitchen, and your boss was wrong, you can still be fired.
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Both previous answers were correct as there is not much you can do. At this point, your focus is on applying for unemployment benefits. Keep in mind that if your employer disputes your benefits and you have a hearing, this is not a forum to "clear your name." It is only designed to see if you are qualified for not. If you get a hearing, I strongly suggest you hire an attorney to assist you.