You're not finished.
Here's an edit and a few explanations below:
You're not using the value range optimally, I think. Pixel art is about the controlled placement of every pixel. Especially in small resolutions such as this, bad pixel placements and being sloppy really shows. I suggest giving love to every little detail. My edit isn't even 50% as carefully done as it would be if it were my own piece.
Dithering is also a really complicated thing to consider in such small spaces where a single pixel takes up so much space. I'd say the smaller the piece of art the less useful dithering is. I tried to use dithering well here but if it were my piece I'd do without dithering aallllmost completely (some fades are necessary).
Try to think about pixel art as pixel art more. Try to think what you can do to maximise the capability of your pixels in small groups (forget about single pixel noise, try to think of them as in groups of two or more of the same color. Check out how I didn't use any single pixels almost anywhere). This is an important point for the pixel art beginner. Think of shapes of pixels and how to make them band as little as possible while also accentuating the forms you want to convey. It's a juggling act between precision-to-form, aa and avoiding banding, essentially.
