The employer is using a table based on your W-4 information that you filed with him/her to do a look-up in a table to guesstimate a proper amount of withholding.
On the W-4, you may have indicated many more exemptions than you were due, in order to increase your take home pay.
If your income paid by the employer was not very large, then it might have been appropriate to withhold nothing - your employer doesn't know your full tax picture (married? kids? other income?) and can do the table look-up based only on what he/she is paying you.
Now that you see the full picture, you can work with your employer to adjust your state tax withholding to approximately cover the expected balance due for next year.
It is a bit odd that 0 exemptions produced no withholding, but it may be that you are in a state that has a high income threshold for taxation. It really varies from state to state - speak to your payroll department.