It's funny because we just had a discussion about tutorials in another topic earlier today.

Tutorials are awesome but remember to figure out WHY certain things are the way they are. Don't just do those 'step by step' tutorials but really delve into why pixel artists do certain things that they do.
I'm not a professional like other artists here on the forums but I'll do what I can to give you some constructive feedback.
ColorAs a beginner myself I always start in greyscale (case and point:
http://azkai.deviantart.com/art/EcoVerse-BlackMarket-Greyscale-WIP-Preview-366889743 ). That's because color can easily cloud our judgement. We can spend hours working on color alone when really it was never a problem to begin with. You're right in thinking that there is WAY too much red in this picture. Now, color is subjective so let me tell you why I personally think there's too much red:
You could easily make this a monochromatic scene and ditch that black for a very dark and desaturated red... however; I really don't think that's what you were originally going for, which is why I'm not recommending it. Red is one of the most powerful colors we can work with and it's one of the most saturated colors found in nature. Remember that saturation will draw the eye to it... so right now, because everything is SO saturated, the eye doesn't know where to look.
To learn more about color I highly suggest this DVD
http://www.thegnomonworkshop.com/store/product/472/color-Theory%3A-The-Mechanics-of-color#.UZ-_JrVUWAg A little pricey to some but well worth it. And since we're on a tutorial kick today, here's a pretty handy tutorial as well:
http://purplekecleon.deviantart.com/art/How-I-See-Color-A-Tutorial-184642625 (But not a replacement for that DVD. That DVD is simply amazing and no tutorial or article I have found can touch it or do it justice.)
When you do work with color later, try figuring out what your focus is. Perhaps it's the lonely flame in the corner. That, then, can be the most saturated part. (Saturation is useful for all sorts of things, not just directing the eye.)
ErrorsYou have some banding situations going on, particularly on the bed. As well, I assume you want that checkerboard pattern to be the pattern that appears on the bed, however; there's no 'feel' to the sheets or pillows... they look incredibly flat and have no texture.
Even very simplistic pixel art still typically gives a feeling of texture since, as humans, we imagine ourselves touching and interacting with things--especially in games and what not.
Also keep in mind that the light coming in from the window would be effecting the color of things most likely.

Those are just a few things I can think of off of the top of my head. Good start and keep at it.