To put it another way, first of all the federal tax rate that applies to long-term capital gains is determined by your taxable income, not gross income. But it's based on your total taxable income, including the capital gain. Did you include the capital gain when you looked at the tax brackets?
Also, most states do not have lower tax rates for long-term capital gains like the federal tax does. So for your state tax, the long-term capital gain is just additional income that is taxed at the regular rates.
