Flat Spectrum Radio Quasars (FSRQs) and BL Lac objects detected in the first three months of the Fermi survey neatly separate in the gamma-ray spectral index vs gamma-ray luminosity plane. BL Lac objects are less luminous and have harder spectra than broad line blazars. We suggest that this division has its origin in the different accretion regimes of the two classes of objects. Using the gamma-ray luminosity as a proxy for the observed bolometric one we show that the boundary between the two subclasses of blazars can be associated with the threshold between the regimes of optically thick accretion disks and of radiatively inefficient accretion flows, which lies at an accretion rate of the order of 0.01 the Eddington rate. The spectral separation in hard (BL Lacs) and soft (FSRQs) objects can then result from the different radiative cooling suffered by the relativistic electrons in jets propagating in different ambients. We argue that the bulk of the most luminous blazars alread detected by Fermi should be characterised by large black hole masses, around 10^9 solar masses, and predict that lowering the gamma-ray flux threshold the region of the alpha_gamma-L_gamma plane corresponding to steep spectral indices and lower luminosities will be progressively populated by FSRQs with lower mass black holes, while the region of hard spectra and large luminosities will remain forbidden.