What kind of shoes are you wearing? If they are regular tennis/running shoes, I would guess that they are not stiff enough.
Numbness like you describe comes from pressure on the nerves in your feet. It is also a common complaint of "clipless" pedals (the kind that egages with a cleat on the shoe). The usual remedy is a slight movement of the cleat position.
I would recommend that you look into getting some shoes made for cycling. You don't have to go the route of clipless pedals, but the stiffer sole will give you more support and likely cure the numbness. You'll also get a better transmission of power as a side benefit.
Cheers,
Jamie