Ultrasound attenuation is caused by absorption and scattering in tissue and is thus a function of tissue composition, hence its imaging offers great potential for screening and differential diagnosis. In this paper we propose a novel method that allows to reconstruct spatial attenuation distribution in tissue based on computed tomography, using reflections from a passive acoustic reflector. This requires a standard ultrasound transducer operating in pulse-echo mode, thus it can be implemented on conventional ultrasound systems with minor modifications. We use calibration with water measurements in order to normalize measurements for quantitative imaging of attenuation. In contrast to earlier techniques, we herein show that attenuation reconstructions are possible without any geometric prior on the inclusion location or shape. We present a quantitative evaluation of reconstructions based on simulations, gelatin phantoms, and ex-vivo bovine skeletal muscle tissue, achieving contrast-to-noise ratio of up to 2.3 for an inclusion in ex-vivo tissue.