The process of rendering high dynamic range (HDR) images to be viewed on conventional displays is called tone mapping. However, tone mapping introduces distortions in the final image which may lead to visual displeasure. To quantify these distortions, we introduce a novel no-reference quality assessment technique for these tone mapped images. This technique is composed of two stages. In the first stage, we employ a convolutional neural network (CNN) to generate quality aware maps (also known as distortion maps) from tone mapped images by training it with the ground truth distortion maps. In the second stage, we model the normalized image and distortion maps using an Asymmetric Generalized Gaussian Distribution (AGGD). The parameters of the AGGD model are then used to estimate the quality score using support vector regression (SVR). We show that the proposed technique delivers competitive performance relative to the state-of-the-art techniques. The novelty of this work is its ability to visualize various distortions as quality maps (distortion maps), especially in the no-reference setting, and to use these maps as features to estimate the quality score of tone mapped images. © 2019 IEEE.