The tunneling magnetoresistance TMR of Fe/MgO/Fe junctions is strongly diminished by small O concentrations in a single partially oxidized FeO interface layer, as is found by first-principles transport calculations. By modeling the electronic transport through the disordered FeO layer within a supercell approach, the effect is traced back to a significant reduction of specular contributions to the conductances of the parallel configuration of the lead magnetizations. These findings bring theoretical TMR ratios closer to their experimental counterparts and highlight the importance of ordered interfaces for large TMR ratios.