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First, you didn't have to take the polygraph. If your employer led you to believe otherwise, it is already in violation of the Employee Polygraph Protection Act.
The questions about ever doing anything dishonest before were so-called "probable-lie control questions." Your denials in response to them were secretly expected to be less than fully truthful. These questions are intended to produce a physiological reaction that can be compared to any reaction(s) to the relevant questions (in this case, about the missing money). Had you shown a stronger reaction to the "control" questions, you would have passed. It seems unlikely that making admissions about past dishonesty would have helped you to pass the polygraph. On the contrary, the more candidly and fully one answers the "control" questions, and as a consequence feels less anxiety when answering them, the more likely one is to wrongly fail.
You won't have to take a re-test, either. You have the right to refuse, and under the Employee Polygraph Protection Act, your employer is prohibited by law from taking any adverse action against you for your refusal (or for the results of your first, failed polygraph). Employers who violate this law open themselves to a lawsuit, and some have had to pay substantial (as much as seven figures, in some cases) damages to employees who brought suit under the Act. You might wish to consult with a lawyer with a background in labor law to discuss your options. If you don't know one, Martindale's "Lawyer Locator" service may be helpful for finding one near you:
I recently had to take a polygraph regarding missing money from where I work. I am not working in some government job or anything else close to that. I work pretty much as a minimum wage worker, couple of months ago, had to work with someone 1 day that was training, she was counting the money and doing most of the paper work, while I was out of the room doing some emails and faxing. When it came time for the final inventory, there was money short. Nothing could be proved from the video surveilance so there was 3 of us that had to take a polygraph. I know I didn't do it but yet they told me I failed miserably. After thinking about it for awhile, think I might have the reason. Question is, on the pre test interview and then questions. After you tell the person doing the test anything that might affect the answers, when they ask during the test if you did anything dishonest before, do you say no or yes. Was led to believe that having admitted to the minor stuff, wasn't what they were looking for and going over the pretest questions, when they asked that, I said no. never once told me that I should answer yes. Was just wondering if I should have answered yes to any question like that since I may have to take another test?