I got a new 5 gallon tank and put cycled water in it from a pet store.
Apparently I didn't wash the gravel enough, and it's leaving a murkyness in the water. So how do I fix the water without reversing the cycled water?

That will be a tough cookie to deal with if you haven't thoroughly wash the substrate. The way to deal with this is keep changing the water every other day if you wish immediate results. You may use some crushed charcoal temporarily added to your filter if your dealing with FW tank. Make sure you wash the charcoal thoroughly.