It is a little difficult from your description to understand what area of the eye you are talking about. Black eye is generally caused due to bruising around the eye and it generally heals after some time. The purple spot you mention may be just the portion of the black eye that did not heal properly. It may be a result of blood capillaries that were bruised when you had a black eye. The skin around the eye is generally very fragile and can get damaged easily. If you have a translucent skin, the discoloration will show up more prominently.
Some natural home remedies can be tried to deal with the purple spot underneath your eye. Mix lemon juice and glycerin and apply it on the spot. You can also apply a paste of turmeric and curry leaves on the affected area and wash your face after about 10 minutes. A paste of saffron and honey can also treat the colored spot. You can also rub cucumbers to on the spot. Take slices of cucumber and apply it over the affected area each morning. Applying aloe vera gel may also be helpful to fade the spot under your eye.
Do apply moisturizer on the purple spot so that the skin looks plump and healthy. A dry skin is thinner and therefore and the spot will look more prominent on a dry skin. You can also use an exfoliant so that it helps thicken the skin under the eye by replacing old dead cells and replacing them with new healthier cells and additional collagen. A thicker skin under the eye is more likely to conceal the discoloration you are seeing. With growing age the skin around the eye keeps going thinner, so it is important to keep the skin well hydrated with proper creams with rich nutrients.
You can also try to camouflage the purple spot with a bit of make-up. Try a light yellow concealer under your foundation. Since yellow and purple color cancel out each other, a sparing use of yellow concealer on the purple spot will help hide it and make it less noticeable. Do take care not use too much of concealer as it may give a brown or ashen look. Also, use the concealer only on the purple spot, and always under the foundation.
If the purple spot shows no sign fading of going away, you can visit a dermatologist and ask for proper medical advice to deal with it.
answered by M W