We investigate the Pt thickness dependence of spin-orbit torques (SOTs) in Co/Pt layers grown on single crystalline SrTiO3 and LaAlO3 and amorphous SiO2 substrates. We measure the SOT-induced effective damping-like fields and spin Hall magnetoresistances of the Co/Pt (t(pt)) samples, where t(pt) varies from 0.5 to 5.5 nm. We find that the Co/Pt layers grown on the single crystalline substrates show weaker thickness dependence of the SOT than the samples on the SiO2 substrate, which cannot be explained by the conventional bulk spin Hall effect in the Pt layer. This indicates that there is a non-negligible interfacial SOT originating from the Pt/substrate interface, which is more pronounced for thinner Pt. These results provide a way to design SOT material structures with enhanced SOT efficiency by incorporating interfacial SOT. (C) 2022 Author(s).