Dye-sensitized semiconductors are promising materials for applications in Grätzel solar cells. Here we are interested in the electron injection into the semiconductor and the initial phase of the electron transport towards the anode. We show that the charge transport in the nanostructured active solar cell material can be very different from that in nonsensitized semiconductors. For ZnO an electron-cation complex is formed within 5 ps which causes fast charge recombination. Moreover, the electron mobility is significantly decreased even after the dissociation of the complex (100 ps) due to strong electrostatic interaction between injected electrons and dye cations. In contrast, sensitized TiO2 nanocrystals do not suffer from this problem due to their high permittivity efficiently screening the charges. We believe that the described processes are responsible for the different power conversion efficiencies of TiO2 and ZnO-based Grätzel cells.