If you ask me, this "You didn't put any effort into this" is a cop-out. Clearly he did put some effort into them, or he wouldn't have completed 4 pieces, each of which look like something, fundamentally. It's true they look simplistic and childish, but that just means he doesn't know how to make things look as they should. They are expressive and creative in nature.
How can you refine something until you know how it's supposed to look and why? Sit a random person down in front of an advanced math problem with no guidance and you'll be lucky if they write anything at all down after 10 minutes of frustration. That doesn't mean they didn't try. Why do people expect newbies to art to be any different?
And that seems to be the main problem... you can't really do pixel art until you know art in general. The suggestion to hit the books and tutorials is a good one, but where to start? First, read up on art theory. A good book is "drawing on the right side of the brain." It talks about how you should learn to draw "what you see" rather than simplistic symbols you've come to associate with what you are trying to draw. Also, look at tutorials concerning color choice, and definetly shading/highlighting tutorials. As for what to practice... start by drawing, coloring, and shading basic shapes such as a sphere, cone, etc. that can easily be compared to references and reality. Once you can do that easily, those skills will transfer over to the more complicated things like your jellyfish's head.
Try these two links for starters. . .
http://www.itchy-animation.co.uk/tutorials/light01.htmhttp://itchstudios.com/psg/art_tut.htm