Compressed sensing (CS) is an efficient technique to acquire sparse signals in many wireless applications to, e.g., reduce the amount of data and save low-power sensors batteries. This paper addresses efficient acquisition of sparse sources through quantized noisy compressive measurements where the encoder and decoder are realized by deep neural networks (DNNs). We devise a DNN based quantized compressed sensing (QCS) method aiming at minimizing the mean-square error of the signal reconstruction. Once trained offline, the proposed method enjoys extremely fast and low complexity decoding in the online communication phase. Simulation results demonstrate the superior rate-distortion performance of the proposed method compared to a polynomial-complexity QCS reconstruction scheme.