The aim of this study was to determine the adsorption performance of a petroleum pitch-based activated carbon (PPAC1:3) before and after a post-treatment with H2S. In the first step, a microporous activated carbon (PPAC1:3) with a highly developed porous structure was produced through a chemical activation route with KOH. Afterward, the synthesized activated carbon was thermally treated yielding two different series of functionalized activated carbons: (i) a series of carbons were treated directly with H2S at elevated temperatures (600 °C and 800 °C), and (ii) a series of carbons were generated by combining an oxidation treatment with plasma followed by H2S treatment at elevated temperatures (600 °C and 800 °C). The chemical and structural characteristics of the S-doped and S-/O-co-doped porous carbons were investigated by means of different experimental techniques, such as XRD, RAMAN, FESEM, XPS, TPD, N2, and CO2 adsorption, and finally tested in CO2 and CH4 adsorption at atmospheric and high pressure. The functionalized porous carbons possessed specific surface areas of 2420–2690 m2/g, total pore volume of 1.05–1.18 cm3/g, and sulfur content up to 2.55 atom % (the sulfur content of the original carbon was 0.19%). After a careful analysis of the carbon dioxide and methane uptake at atmospheric (0.1 MPa) and high pressure (4 MPa), adsorption results confirm that the microporous structure is the main structural parameter defining the adsorption performance and, to a lower extent, the surface chemistry. Overall, a significant improvement in the total uptake can be appreciated after the H2S treatment.