I believe studies have shown that humans perform facial recognition principally from the eyes, then the mouth and nose. Babies are drawn to look at people's eyes naturally as they learn to recognise faces. So our brains, more so even then other primates, are basically hard wired to focus on eyes to recognise firstly that it is a face, so it goes to the facial recognition part of our brain, and then whether it it a face that we recognise. So the eyes are, for humans, the most recognisable, and hence important, part of the face.
I've read various evolutionary and developmental reasons for all this.