Again we are in the realms of speculation upon speculation, but Neanderthals didn't have sclera (whites of the eyes) which according to the co-operative eye hypothesis as regards to domesticated hunting dogs allows them to follow our gaze. It does seem odd that Neanderthals didn't try to domesticate them too - surely the first reaction on seeing humans and dogs bring down a mammoth or corral large deer would be 'got to get us some of that', but as sibling comments say we don't know much about them really.