Hi Salad,
Welcome to Pixelation!
Since you're familiar with traditional art methods already I won't even deal with lightsources and such. You're quite fortunate because most of the guys around here start with no art background at all.
In pixel art we do a lot of simplifications of surfaces (reducing large areas that would contain a gradient or lots of detail to one block of colour) and we push certain key details more to make things recognisable. You'll know this as caricaturing or symbolisation I imagine.
Another thing we do in pixel art is making things that are further away darker/less saturated, as well as things that are lower. These are also just methods we use to pass across ideas and not necessarily realistically accurate.
We just lie a lot really.
So let's dig right in to an edit.

I've reduced the amount of colours in your piece and dropped a lot of the saturation.
Cleaned up some of the more busy areas and over emphasized things like the wings and the size of the feathers/fluff.
Made the lower areas, tail and right side of the bird darker in following with typical pixel practices.
Hope this gives you an idea of the kind of things we try to accomplish with pixel art, and that we'll see more out of you.