Ultra-thin amorphous carbon (a-C) films are well established protective coatings of optical fibers. These coatings allow one to prevent degradation of the SiO2 fiber, which occurs due to diffusion of the water and hydrogen molecules into cladding and core. The a-C films typically contain impurities, such as oxygen and hydrogen, which are attached to organic moieties via chemical bonding. The formation of hydrogen- and oxygen-containing functional groups reduces the hermeticity of a-C coatings, and therefore, monitoring these impurities is of great importance. In this work, we develop a method for probing O- and H- containing moieties based on resonance anti-Stokes Raman spectroscopy. We measured Raman spectra of a-C films and observed that anti-Stokes to Stokes ratios of Raman peaks differ from those predicted by Boltzmann law. This effect caused by resonance enhancement of the anti-Stokes Raman scattering in defects of graphite-like crystals. To quantify this effect, we used a resonance factor, which is defined as a ratio of the anti-Stokes and Stokes scattering cross sections. We show that this indicator can be used to assess degree of enrichment/depletion of a-C with O- and H- containing functional groups. Understanding the physical mechanisms of the anomalous anti-Stokes Raman scattering will improve Raman thermometry.