The sulfonated (SO3H-functionalized) carbon nanomaterials were obtained by direct sulfonation of the initial carbon nanofibers and nanotubes. Concentrated sulfuric acid, oleum (20% SO3) and sulfonating mixtures containing 5 wt% MSO4/H2SO4 (98%; M = VO2+, Cu2+, etc.) were used as a sulfating agents. It was shown that the use of MSO4/H2SO4 sulfonating mixtures allows achieving the efficiency of the sulfonation comparable with the case of oleum. Thus, in the case of the most effective sulfonating mixtures containing such ions as VO2+, Cu2+, Fe3+, the values of the sulfur content were 1.2, 1.1 and 1.15 wt%, respectively. The optimal temperature of the sulfonation process was found to be in a range of 180–200 °C. All this provides a high acidity of the obtained materials along with maintaining the textural parameters (specific surface area of ~100 and ~300 m2/g for CNF and CNT, respectively). The structural changes of the materials taking place during the sulfonation process were studied by means of low-temperature nitrogen adsorption, X-ray photoelectron spectroscopy, Raman spectroscopy, high resolution transmission electron microscopy, and both the titrimetric and elemental analyses. According to the data obtained, high efficiency of the sulfonating mixtures is stipulated by the process of oxidative destruction of the surface layer of the carbon material that leads to an increase of its defectiveness thus enhancing the sulfonation efficiency.