By using electron microscopy and X-ray photoelectron spectroscopy (XPS), we show that the structure of support carbon materials—carbon nanofiber (CNF) and carbon nanotubes (CNTs)—affects the electronic state and dimensions of supported platinum particles that display a high catalytic activity in acetylene hydrogenation. Increasing the platinum load of Pt/CNF catalysts from 0.075 to 0.3 wt % results in the enhancement of their catalytic activity, while the selectivity for ethylene diminishes, which we attribute to the enlargement of the platinum nanoparticles. The XPS studies reveal that the platinum exists in, on average, a more oxidized state at the surface of CNTs when compared to CNF. The detection of substantial quantities of the residual chlorine at the surface of the prepared support materials allows us to relate the presence of the platinum in oxidized states to the existence of surface sites differing in quantity and the ability to stabilize platinum at the surface of nanocarbons. In addition, we have established that a fraction of the platinum in Pt/CNT catalysts is located inside of the CNTs. The differences between the states of CNT- and CNF-supported platinum nanoparticles affect catalyst selectivity: the Pt(0.075%)/CNT catalyst exhibits superior selectivity for ethylene hydrogenation than the Pt(0.075%)/CNF catalyst. The enhanced selectivity may be a consequence of the different electronic structures of the platinum in the considered catalysts and faster Knudsen diffusion of acetylene molecules, when compared to ethylene molecules, in CNT channels.