The proximity effect in a heavy metal attached to a ferromagnetic (FM) layer results in varied interface magnetism. In this study, we investigated the critical behavior of the perpendicular exchange bias in a Ru/Pd/Co/Pt/Cr2O3/Pd stacked film, with focus on the influence of the Pt spacer layer. The apparent critical exponent β increases with increasing Pt thickness. We discussed the possible mechanism from the perspective of the induced magnetic moment of Pt and interfacial exchange coupling. The former was explored based on X-ray magnetic circular dichroism, which revealed that the magnetic moment of Pt was almost temperature-independent within the studied temperature regime. This suggests that the interfacial FM moment is stable. The latter, i.e., the reduction of the interfacial exchange coupling by the Pt spacer layer, is a possible cause of the increase in β, as theoretically predicted.