We cannot see your tax return. We do not know what other income you received or if you had enough tax withheld from that income. The usual reason for owing state tax is that you did not have enough withheld from your paychecks---or perhaps from your unemployment. Check all of the data you entered and make sure you did not enter something incorrrectly.
If you did not pay enough taxes on your unemployment during the year, you may have to pay additional taxes on it when you complete your tax return. The IRS, as well as most states, consider unemployment income as taxable income.
The difference between what your tax liability is and what you withheld is the amount you owe. Since you stated that you owe taxes, your tax bracket is higher than the tax withheld on your unemployment.
TurboTax has a great tool that can help you withhold the correct amount of tax on your income sources. Please see Tax Bracket Calculator for a better estimate on what should be withheld.