We evaluate the interactions between a central equal mass binary and a surrounding retrograde circumbinary accretion disk in a three-dimensional, MHD simulation. We find (as widely expected) that the net torque expressed on a retrograde circumbinary disk by the central binary is much (more than two orders of magnitude) smaller than when the disk orbits in the prograde direction. For this reason, unlike the prograde case, there is no gap carved out of the retrograde disk, and accreting fluid can travel directly from the disk to the domain of the binary. For the same reason, retrograde disks do not develop the large-amplitude lumps generically seen near the inner edges of prograde disks. Although not directly treated in this simulation, the finite extent of accretion disks around the individual masses of the binary can lead to shocks between their outer edges and the circumbinary disk, potentially creating a photon signal modulated at the binary orbital period. The spectra of these shocks should peak in the hard X-ray band as is expected for prograde systems, but retrograde systems would not be expected to display a notch in the optical/UV band. Because the disk's angular momentum is directed oppositely to that of the binary, accretion onto the binary causes a rapid increase in eccentricity. Lastly, we discuss the comparative rates of orbital evolution associated with accretion in prograde and retrograde circumbinary disks, finding that the principal contrast is that should be rather greater in the retrograde case.