I didn't know to charge a client Florida sales tax on security guard services, and got audited. Am I still responsible for paying the sales tax on all the invoices that I gave the client.

Typically, yes.

Most sales tax agents for virtually ALL of the states take the attitude that it is YOUR responsibility to know whether you need to charge sales taxes or not. If you fail to collect the taxes, that failure does NOT relieve you of the requirement to PAY the taxes.