We compare the properties of galaxies that form in a cosmological simulation without strong feedback to observations of the z= 0 galaxy population. We confirm previous findings that models without strong feedback overproduce the observed galaxy baryonic mass function, especially at the low- and high-mass extremes. Through post-processing we investigate what kinds of feedback would be required to reproduce the statistics of observed galaxy masses and star formation rates. To mimic an extreme form of ‘preventive’ feedback, such as a highly efficient active galactic nucleus ‘radio mode’, we remove all baryonic mass that was originally accreted from shock-heated gas (‘hot-mode’ accretion). This removal does not bring the high-mass end of the galaxy mass function into agreement with observations because much of the stellar mass in these systems formed at high redshift from baryons that originally accreted via ‘cold mode’ on to lower mass progenitors. An efficient ‘ejective’ feedback mechanism, such as supernova-driven galactic winds, must reduce the masses of these progenitors before they merge to form today's massive galaxies. Feedback must also reduce the masses of lower mass z= 0 galaxies, which assemble at lower redshifts and have much lower star formation rates. If we monotonically remap galaxy masses to reproduce the observed mass function, but retain the simulation-predicted star formation rates, we obtain fairly good agreement with the observed sequence of star-forming galaxies. However, we fail to recover the observed population of passive, low star formation rate galaxies, especially at the high-mass end. Suppressing all hot-mode accretion improves the agreement for high-mass galaxies, but it worsens the agreement at intermediate masses. Reproducing these z= 0 observations requires a feedback mechanism that dramatically suppresses star formation in a fraction of galaxies, increasing with mass, while leaving star formation rates of other galaxies essentially unchanged.