Fast radio bursts (FRBs) are short-lived (~ms), energetic transients (having a peak flux density of ~Jy) with no known prompt emission in other energy bands. We present results of a search for prompt X-ray emissions from 41 FRBs using the Cadmium Zinc Telluride Imager (CZTI) on AstroSat, which continuously monitors ~70% of the sky. Our searches on various timescales in the 20-200keV range, did not yield any counterparts in this hard X-ray band. We calculate upper limits on hard X-ray flux, in the same energy range and convert them to upper bounds for {eta}: the ratio of X-ray to radio fluence of FRBs. We find {eta}<=10^8-10^ for hard X-ray emission. Our results will help constrain the theoretical models of FRBs as the models become more quantitative and nearer, brighter FRBs are discovered.