Unless you had a written contract in which the company agreed to hire you for a specified period of time, you, like most employees, were an at-will employee. That means you can quit at any time for any reason. Similarly, your employer can fire you at any time for any lawful reason and there is not requirement to provide notice or a reason, etc. As long as you received your final paycheck including any earned and unused PTO (not sick leave) or vacation, based on what you stated in your question, you have no case.
If you were an "at will" employee--and most private sector employees are--you can be fired for unfair or untrue reasons. Your employer has no obligation to provide warnings or give you a second chance. I am sorry.
This answer is a general interpretation of the law and is not fact specific to your case. Likewise it does not create an attorney-client relationship. You should seek an attorney for a review of your specific facts and documents. http://www.johnphillipslaw.com
Most private employment in California is "at will". This means you can be terminated for any reason, or no reason at all, at any time so long as it isn't based on discriminatory reasons (i.e. because of race, sex, national origin or another protected classification), or your having engaged in a protected activity, or in violation of the terms of a contract or collective bargaining agreement.
Being “at will” also means that the employer is not required to provide a warning or advance notice of a termination decision and is not required to justify the decision with “good cause.” So, based on the facts you provided there is no basis for suing your employer. Sorry...
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I concur with all of the comments by the responding attorneys here. But to your specific point let me add: if you were an at will employee (no contract, no union, no civil service) your employer had the right to terminate you even if you did not "talk back;" even if you can prove that you did not talk back; and even if the employer knows that you did not "talk back." At will employment can be very brutal and unfair, but it is the law in 49 and a half states.
I am sorry for this loss to you and I wish you well in finding new employment.
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