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.

Note that this polygraph procedure has no grounding in the scientific method. It's sheer pseudoscience, and polygraph chart readings are evidence of nothing. For further reading, see The Lie Behind the Lie Detector.

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:

http://www.martindale.com