You have to take each frame, one by one and lower the quality and redo it. If you use photoshop, save it as JPEG and it'll give you the option to change quality. If you are trying to use an animation saved from a website, you'll have to printscreen and crop each frame. If you can catch it. ^_^.
I think that's how anyway. Since my avatar is only two frames, it's quality is pretty low.