In order to investigate the importance of different proposed quenching mechanisms, we use an indirect method to estimate gas masses for ~62,000 SDSS DR7 galaxies. We infer gas surface densities from dust column densities as traced by extinction within the fibre, applying a metallicity correction to account for varying dust-to-gas ratios. We find that both gas fraction and star formation efficiency (SFE) decrease moving away from the star forming main sequence (MS) towards quiescence for all galaxy masses. We further show that both quantities correlate similarly strongly with the departure from the MS, implying the need for any physical model of quenching to invoke a change in $both$ gas fraction and SFE. Our results call for a better understanding of the physical processes driving the decrease in star formation efficiency, which has received relatively little attention in the theory of quenching until now.