A method, how electrons can be directly accelerated in intense laser fields, is investigated experimentally and discussed with numerical and analytical simulation. When ultrathin foil targets are exposed with peak laser intensities of ~ 1x1020 W/cm2 , slow electrons ( ~ keV kinetic energy), that are emitted from the ultrathin foil target along laser propagation direction, are post-accelerated in the transmitted laser field. They received significant higher kinetic energies (MeV), when this interaction was limited in duration and an enhanced number of fast electrons were detected. The decoupling of the light field from the electron interaction we realized with a second separator foil, blocking the transmitted laser light at a particular distance and allowing the fast electrons to pass. Variation of the propagation distance in the laser field results in different energy gains for the electrons. This finding is explained with electron acceleration in the electromagnetic field of a light pulse and confirms a concept being discussed for some time. In the experiments the effect manifests in an electron number amplification of about 3 times around a peak at 1 MeV electron energy. Measurements confirmed that the overall number in the whole bunch is enhanced to about 109 electrons covering kinetic energies between 0.5 to 5 MeV. The method holds promise for ultrashort electron bunch generation at MeV energies for direct application, e.g. ultra-fast electron diffraction, or for injection into post accelerator stages for different purposes.