If it looked like a European field mouse, it was probably a deer mouse - Peromyscus maniculatus. Apodemus is an Old World genus. I'd be surprised if there were any running around in North America. :)

Alternatively it may have been a vole(Microtus spp.), which are commonly called 'field mice' in North America. Voles have smaller eyes than mice because they are diurnal where mice are primarily nocturnal.

/biology class ;D