An inherent part of the "freemium" model is the "free" bit. The point is to entice people in further. It's up to you the service offerer to make the pay service so compelling that people want to switch to it. It's completely wrongheaded to look at the people who aren't willing to pay and say they are the problem, or say or imply that they are leaching or ungrateful.

You are enticing people in, if you don't have what it takes to then transform them into paying customers, and you don't want to pay for their ongoing use, then perhaps you should switch to a free-trial instead of a free service.