Well, if you apply a shadow and then zoom in on it you will notice that it is a bitmap and will pixellate if using at very large sizes. Also, it is basically a gradient, so this may well affect the number of colours used. The same applies using the feather tool too.
You might be better advised to make a copy of the object to which you wish to apply a shadow, colour it a mid to light grey and place it behind the original object, placed slightly off from the original position. This will only add one extra colour (unless you have already used that colour for another object in your design).
Bob.