We experimentally show evidence for the presence of spin accumulation in localized states at ferromagnet-silicon interfaces, detected by electrical Hanle effect measurements in CoFe/$n^{+}$-Si/$n$-Si lateral devices. By controlling the measurement temperature, we can clearly observe marked changes in the spin-accumulation signals at low temperatures, at which the electron transport across the interface changes from the direct tunneling to the two-step one via the localized states. We discuss in detail the difference in the spin accumulation between in the Si channel and in the localized states.