This has 57 colors, which is far more than needed. Some colors are only used on a single pixel and are not used anywhere else. I think this can be made very close to the same using only 12-16 colors. There's a lot of banding too. This tutorial covers a lot of common problems in pixel art and tells how to avoid them- link
I agree with tanuki, i've read through every tutorial on that page and it's helped me a lot, go there and see for yourself.