We have experimentally characterized the light-output response of a deuterated trans-stilbene (stilbene-d12) crystal to quasi-monoenergetic neutrons in the 0.8 to 4.4 MeV energy range. These data allowed us to perform neutron spectroscopy measurements of a DT 14.1 MeV source and a PuBe-239 source by unfolding the impinging neutron spectrum from the measured light-output response. The stilbene-d12 outperforms a H1-stilbene of similar size when comparing the shape of the unfolded spectra and the reference ones. These results confirm the viability of non-hygroscopic stilbene-d12 crystal for direct neutron spectroscopy without need for time-of-flight measurements. This capability makes stilbene-d12 a well suited detector for fast-neutron spectroscopy in many applications including nuclear reaction studies, radiation protection, nuclear non-proliferation, and space travel.