In carbon-containing alloys, the energetic stability of vacancy-carbon (v-C) clusters plays a key role in the post-irradiation damage recovery. So far, all interpretations of post-irradiation annealing experiments are based on the theoretical knowledge established for the iron-carbon alloy. For the interpretation of high-Cr steels, the stability of v-C clusters in the presence of a solid solution background is essential. Therefore, a simple and efficient model to estimate the stability of v-C clusters in random solid solution alloys is proposed. The model is parameterized for the Fe-Cr-C alloy using density functional theory. The results are discussed accounting for available experimental evidences.