Pulling a fire alarm (accidental or not) can easily be deemed misconduct sufficient to support a termination.
As an at-will employee, you can quit at any time for any reason, you can be fired for any reason, a rotten reason, or no reason, except unlawful discrimination. If you do not have an employment contract or union to represent you, your recourse is limited. Discrimination based on age, gender, race, religious beliefs etc.... may give rise to a different answer.
You might find my Legal Guide helpful "Workplace Discrimination: A Basis for Wrongful Termination Claims"
You might find my Legal Guide helpful "How to Choose a Lawyer for you.”
You might find my Legal Guide helpful "What Do I Tell My Lawyer"?
No one can know what the record is in the case because online we cannot find out any details. Check with a lawyer in your locale to discuss more of the details.
If you have a discrimination theory about retaliatory discharge or hostile workplace conditions you'll need a lawyer. Religious belief, age, gender, race etc. all are discriminatory reasons for which you cannot be legally fired and upon which you might base a wrongful termination suit.
Good luck to you.
NOTE: This answer is made available by the out-of-state lawyer for educational purposes only. This observation is not like a communication with a lawyer with whom you have an attorney-client relationship along with all the privileges that relationship provides.
Employer's cannot fire someone fore reasons based on discrimination. Barring that, they can fire you for any reason, or no reason at all
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.
What you really need to evaluate is why the employer would have treated you more harshly than other similar employees. IF it was because of your race or gender or religion or because of a disability, etc., then you may have a legal claim against your former employer. If not, you probably have not claim.
Speak to an employment lawyer to go through the issues. YOu can also check out my employee rights blog at www.takethisjobnshoveitblog.com.