Compact groups (CGs) provide an environment in which interactions between galaxies and with the intra-group medium enable and accelerate galaxy transitions from actively star forming to quiescent. Galaxies in transition from active to quiescent can be selected, by their infrared (IR) colors, as canyon or infrared transition zone (IRTZ) galaxies. We used a sample of CG galaxies with IR data from the Wide Field Infrared Survey Explorer (WISE) allowing us to calculate the stellar mass and star formation rate (SFR) for each galaxy. Furthermore, we present new CO(1-0) data for 27 galaxies and collect data from the literature to calculate the molecular gas mass for a total sample of 130 galaxies. This data set allows us to study the difference in the molecular gas fraction (Mmol/Mstar) and star formation efficiency (SFE=SFR/Mmol) between active, quiescent, and transitioning (i.e., canyon and IRTZ) galaxies. We find that transitioning galaxies have a mean molecular gas fraction and a mean SFE that are significantly lower than those of actively star-forming galaxies. The molecular gas fraction is higher than that of quiescent galaxies, whereas the SFE is similar. These results indicate that the transition from actively star-forming to quiescent in CG galaxies goes along with a loss of molecular gas, possibly due to tidal forces exerted from the neighboring galaxies or a decrease in the gas density. In addition, the remaining molecular gas loses its ability to form stars efficiently, possibly owing to turbulence perturbing the gas, as seen in other, well-studied examples such as Stephan's Quintet and HCG 57. Thus, the amount and properties of molecular gas play a crucial role in the environmentally driven transition of galaxies from actively star forming to quiescent.