You used 16.7 million colors to get the drop shadow. In this mode, you have access to a large number of colors to create a smooth gradient in the shadows as well as the fact that the 16.7 million color mode has a true transparency mode which allows partial transparency in place of GIF's one color/total transparency mode.
When that image is converted to 256 colors for a GIF image, the transparency of the shadow is lost and the program converts to solid colors for the shadow and drops the number of colors to 256.
If the background color for the shadow was white, and the shadow color is black, then the shadow created will be shades of gray. If the white background is made transparent, and the image placed on a red background in the web site, you'll still have a gray shaded shadow on a red background, which looks pretty awful.
In the example above, if your webpage background was red, then the shadow should be originally created as black to red, You create the shadow to blend in with your website's red background. If you use any color other than red, your shadow will look trashed once it lands on that web page's red background.
If the background is patterned, or you want to use the same image on different colored backgrounds, use a solid shadow with a dark color, which is a different color from the foreground image.
Select the item you're wanting to have a shadow, invert and give it a shadow of a dark color with the brush Paper Texture set to Dither 50% . The idea here is to have 50% of the shadow transparent, and 50% of the shadow color. It'll show enough of the color below to appear to be a semi-transparent shadow. (There are other dither rates, 75 and 25 % for darker and lighter shadow effects.)