This is a valid question, perhaps the author failed to elaborate or was just fluffing the story a bit. I remember watching a anthropologist discuss the techniques on producing cutting blades from stone ( which isn't as easy as you would think ). One wonders if modern humans where just better at it - but I'd like to see the evidence.
Seeing the evidence is a simple task. Tools found with modern humans are far, far superior to those found with Neanderthals. If you literally want to see for yourself, just go to a museaum (such as the Smithsonian) where you can see artifacts found with Neanderthals and compare them to artifacts found with modern humans.
And of course, if I were being facetious, I would note that modern humans have built skyscrapers and sent spacecraft to the moon in less time than the Neanderthals spent trying to perfect the sharpening of flints..