Neutrons with energies between 0.1-10 MeV can significantly impact the Soft Error Rate (SER) in SRAMs manufactured in scaled technologies, with respect to high-energy neutrons. Their contribution is evaluated in accelerator, ground level and avionic (12 km of altitude) environments. Experimental cross sections were measured with monoenergetic neutrons from 144 keV to 17 MeV, and results benchmarked with Monte Carlo simulations. It was found that even 144 keV neutrons can induce upsets due to elastic scattering. Moreover, neutrons in the 0.1-10 MeV energy range can induce more than 60% of the overall upset rate in accelerator applications, while their contribution can exceed 18% in avionics. The SER due to neutrons below 3 MeV, whose contribution has always been considered negligible, is found to be up to 44% of the total upsets in accelerator environments. These results have strong Radiation Hardness Assurance (RHA) implications for those environments with high fluxes of neutrons in the 0.1-10 MeV energy range.