The stopping power of antiprotons in atomic and molecular hydrogen as well as helium was calculated in an impact-energy range from 1 keV to 6.4 MeV. In the case of H2 and He the targets were described with a single-active electron model centered on the target. The collision process was treated with the close-coupling formulation of the impact-parameter method. An extensive comparison of the present results with theoretical and experimental literature data was performed in order to evaluate which of the partly disagreeing theoretical and experimental data are most reliable. Furthermore, the size of the corrections to the first-order stopping number, the average energy transferred to the target electrons, and the relative importance of the excitation and the ionization process for the energy loss of the projectile was determined. Finally, the stopping power of the H, H2, and He targets were directly compared revealing specific similarities and differences of the three targets.