Use a hot oil treatment.

My hair is dark brown and "grabs" color. I use light brown and if you wanted a more highlighted look (depending on where and the pattern of your grey), you could even use a blond shade.

You could do 4 consecutive washes, lather rinse repeat, this will give you immediate lightening until time does it's job.

Back in the day when I did my own hair I had a couple "oops" results and did what mitch suggests. It helps!

I've had really good luck washing consecutively with Prell. Yep, the green stuff.

I also use non-permanent color, and my hair always looks too dark brown at first. In about three days, the color lightens on its own without any special washing. Why not wait and see if you have the same experience?

I would use some dawn dishwash soap. I know, awful for your hair, but you want to get some of it out. It will fade out naturally, you are just trying to hurry it up a little.

My natural color is a dark brown. I use a non-permanent color and find the colors labeled any sort of "dark" brown were too dark. I now use a "medium" brown shade and it's about right. It does gradually lighten up a little till it's time to re-do.

When you use mitch's method, leave the shampoo on for a minute before you rinse.

I've heard you can use prell, dawn and also a clarifying shampoo. They may work, but that is going to be hard on just colored hair. There is also a product called "oops". If you use any of these, I would deep condition. You might not be able to re-color hair for a few days.

As a person who owned a salon, let me say that it's very easy to remove. Wash the front of your hair with a liquid dishwashing soap. Leave it on for 15 minutes and then rinse. You'd be better served if you used a lighter shade. Coloring your own hair is tricky as it looks so easy on t.v.
You have two choices
use a semi permanent tint or use a permanent tint. The first fades off with washing and the second stays until you need a touchup.
It's not a good idea to touch up just one area of the head as it's almost impossible to choose a color that is an accurate match to the rest of your hair. In the salons we use several colors plus grey magic which is a small bottle of a medium that helps to keep the color on the gray.
Next time buy a neutral medium brown shade, I say neutral so you won't have any green or gold caste to your hair. If you like a warm tone use it. I wouldn't suggest using a cool tone on any of the brown choices.
If worse comes to worse and you can't get it out, sprinkle some talc or baby powder in your dark area and brush it through. Works like a charm.

I lathered and rinsed four times with dawn. It's still wet. I see a little more gray at my temples, but the rest of my head -- the part that was brown already -- still seems pretty dark.

If my brain were as absorbent as the hair on top of it I'd be much smarter.

I did have to keep an appointment this morning before trying the fix. I styled my hair "smaller", ironing it flat and then sweeping it back with a headband. This makes it feel less visible and more ok.

Thanks for the help. I viewed a couple of oops videos. It seemed like it's better to wait, since this is a temporary color, but it's interesting to see a home product that will remove color mistakes. I might get more adventuresome.