Flat Spectrum Radio Quasars (FSRQ) are the most powerful blazars in the gamma-ray band. Although they are supposed to be good candidates in producing high energy neutrinos, no secure detection of FSRQs has been obtained up to now, except for a possible case of PKS B1424-418. In this work, we compute the expected flux of high energy neutrinos from FSRQs using standard assumptions for the properties of the radiation fields filling the regions surrounding the central supermassive black hole. We obtain as a result that high energy neutrinos are naturally expected from FSRQs in the sub-EeV-EeV energy range and not at PeV energies. This justifies the non-observation of neutrinos from FSRQs with the present technology, since only neutrinos below 10 PeV have been observed. We found that for a non-negligible range of the parameters the cumulative flux from FSRQs is comparable to or even exceeds the expected cosmogenic neutrino flux. This result is intriguing and highlights the importance to disentangle these point-source emissions from the diffuse cosmogenic background.