Yes, you should file for unemployment -

If an Employee Was Fired

Fired employees can claim unemployment benefits if they were terminated because of financial cutbacks or because they were not a good fit for the job for which they were hired. They can also receive unemployment benefits if the employer had a good reason to fire the employee, such as being late for work several times, but the infractions were relatively minor, unintentional, or isolated.

http://www.nolo.com/legal-encyclopedia/unemployment-benefits-contesting-employees-claim-30348.html