We study the effect of the extreme environment in Hickson Compact Groups (HCGs) on the molecular gas mass, M_H2_, and the star formation rate (SFR) of galaxies as a function of atomic hydrogen (HI) content and evolutionary phase of the group. We selected a redshift-limited (D<100Mpc) sample of 88 galaxies in 20 HCGs with available atomic hydrogen (HI) VLA maps, covering a wide range of HI deficiencies and evolutionary phases of the groups containing at least one spiral galaxy. We observed the CO(1-0) and CO(2-1) lines with the IRAM 30m telescope for 47 galaxies. Together with literature data, our sample contains CO(1-0) spectra for 86 galaxies. We derived the far-infrared (FIR) luminosity L_FIR_ from IRAS data and used it as a tracer of the star formation rate (SFR). We calculated the HI mass, M_HI_ L_FIR_ and M_H2_ deficiencies, based on the values expected from L_B_ and L_K_ in isolated galaxies from the AMIGA sample. We limited our statistical analysis to spiral galaxies, since the large number of upper limits did not allow drawing strong conclusions about M_H2_ and L_FIR_ in early-type galaxies.