In this study, we analyze the correlation between magnetization and magnetoresistance of perpendicularly anisotropic [Co/Pd] multilayered films with different thicknesses of Pd layers tPd = 0.6–2.0 nm in a wide range of temperatures, T = 4–300 K. We revealed that electron scattering by magnons makes a significant contribution to the magnetoresistance of the multilayers regardless of the layer thickness. Contrary to expectations, the effect of magnon magnetoresistance (MMR) increases with decreasing temperature below T = 50 K in the films with tPd = 0.8 and 1.0 nm. The revealed low-temperature MMR increase, which is most pronounced in the [Co0.5/Pd1.0] multilayers, is associated with the enhanced magnon excitation due to antiferromagnetic exchange coupling between the Co layers. The latter ensures an atypical shape of the magnetization curves of the [Co0.5/Pd1.0] multilayers at low temperatures in a perpendicular magnetic field, which combine a quadratic hysteresis loop of a perpendicularly anisotropic ferromagnet and an anomalous magnetization drop resulting from a violation of the ordering of magnetic moments and their amplified oscillations initiated by the interlayer exchange coupling.