You didn't say what kind of "football" you propose to play on a concrete field. I can't imagine playing American, Canadian, or Australian football on a concrete surface. Football players have to be a little crazy, but anyone who would be willing to play football on concrete or asphalt should be committed forthwith.
Well, as we generally call a "football field" a pitch in British English, and pitch doesn't refer to the surface, we would still call this a pitch. To differentiate on the basis of surface, we would have to name it (e.g. concrete pitch): Getting tripped on a concrete pitch isn't fun
On a bumpy concrete pitch still wet from overnight rain, a pick-up game of football is under way