Your retina has two kinds of light-sensing nerves: cones and rods. Cones are responsible for color vision, i.e. hue, while your rods handle differences in the value, as in how bright it is.
Humans have adapted to have cones mostly in the center of the eye (which corresponds to what you're looking directly at), where the most distinguishing color information is needed. It's not often that you'd use your peripheral vision to identify the actual color of something, and this explains why you're seeing a difference between pink and red. The intensity of the color is correct, but you aren't able to identify the hue because of a lack of cone nerves.
So yes, this is normal. A fun trick (and also totally helpful if you have a messy room) is to look a foot or so above the floor when you're walking in the dark. It allows you to see what you're walking on better, since you need intensity receptors more than color receptors.