This is a nice piece, but it looks like it would have taken forever to make! 

size of this piece. 

When I take a look at your pallete, probably the first thing that comes to
mind is the colour count. There are tons of colours there! In pixel art,
people tend to conform the unspoken rule of video game restriction.
Which one of those 'rules' is a low colour count. People won't force you,
but will always suggest tweaking and reducing colours where possible.

My second thought on your palette would be the the hues of those colours.
What you've made there is called a 'straight ramp'. Simply put, they're colour

ramps that literally just increase or decrease in the brightness of the colour.
A good technique used by the majority of pixel artists on this website is

something called 'hue shifting'. All you have to do is slide the brighter hues

in the direction that will get to yellow the fastest, and slide the darker ones

towards purple in the direction that will also get there the fastest. Not only
does hue shifting increase interest in your piece, it makes for more realistic

shading (not always).

Before you go any further on this piece, I highly recommend you check out
Cure's pixel art tutorial here.