Well think about it--an elliptical requires absolutely no foot movement to operate. Even riding a bicycle or walking, while in principle similar, requires you move and stretch your foot muscles depending on the terrain you're on, and the velocity you're traveling. An elliptical (unless it has pivoting pedals) really does require that. You don't need to feel like there's something wrong with you--it's normal (and expected) your feet will go numb after a while.
As for how to mitigate the numbness, if adjusting things doesn't work you may just have to resort to wiggling your toes while you peddle, or shifting the weight to different areas of your feet as they become numb (ball to heal to toe to blade--or something).