I use a product made by Max Factor, it comes in a lipstick tube and it's white. They have other shades if you are afraid of looking like a raccoon but the women in my family and I have been using white under our eyes since we were old enough to wear make up. I dab the white "lipstick" under my eyes and then on the upper lids. I then work it into my skin with my middle finger. To conceal the whiteness a bit, I use powder applying it just under the lower lid and upper cheeck where I've applied the concealer and to the sides of my face, cheek to eye. This seems to smooth out any flaws.
The whole concept of the white is like painters using "Gesso" so if you are familiar with that, it won't seem so weird. You can try the more conventional approach of foundation but my aunts, my mom, and myself have all reaped the benefits of using white as our concealer (we used to use a product called "White White" by Maybelline but they have discontinued it).
After you have applied the concealer and the powder then you can put on your eyeshadow...I suggest soft colors. You will see that your eyes are now much brighter. Even without shadow, sometimes I will just gently brush some blush around my lids to even out all the color and I look refreshed and healthy.
Max Factor is getting hard to come by but you can still purchase it at K Mart. The product that I am talking about is about $4.50. Again, it is white and in a lipstick tube.
Good luck to you!