If you paid for it, you were willing to pay at least the asked amount. In a "pay what you want" scheme, your willingness to pay is something between infinity and what you wind up paying. If you don't buy a thing, your willingness to pay is something below the price being asked.
There's no magic. It's an immediately available revealed-preference system - you either pay or you don't. I won't disagree that the availability of a free, well-functioning, DRM-free, easily available alternative reduces people's willingness to pay for locked-in, degraded, or even available-but-overpriced alternatives. That said, we live in a world where the piracy alternative exists, whether people like it or not.
Adjust your business model accordingly. Valve is making a killing selling software via Steam.