Within the framework of the ATLAS-MPX project, the ATLAS-MPX detectors (based on Medipix2 silicon devices) are covered with converting layers of (6)LiF and polyethylene (PE) to make them sensitive to thermal and fast neutrons, respectively. Two ATLAS-MPX reference detectors were exposed to two calibrated neutron sources, (252)Cf (2.2 MeV mean neutron energy) and (241)AmBe (4.08 MeV mean neutron energy), in order to determine their fast neutron detection efficiency. Measurements were performed at low energy threshold (similar to 8 keV) and high energy threshold (similar to 230 keV). Fast neutron detection efficiency is primarily achieved via the use of a 1.3 mm thick polyethylene (PE) converter. Recoil protons from the elastic collision between neutron and hydrogen are detected from their tracks in the 300 mu m thick silicon pixel detector. Calibrated neutron sources were placed at different distances from the detectors, both separately and simultaneously in order to obtain single and superposed neutron energy spectra. As expected, the neutron detection efficiency in the PE layer increases when the neutron mean energy increases due to the decrease of proton self-absorption in the PE converter itself. The variation of the cluster size as a function of the proton and alpha energy (at low energy threshold) was also studied for better understanding of the neutron response using the PE converter. The determination of the ratio of the fast neutron responses in each detector region at high energy threshold made it possible to establish a relation between the ratios and the mean neutron energy. At low energy threshold, a relation between the neutron energy spectrum and the cluster size distribution of heavy charged particles has been established.