Surgical telementoring systems have gained lots of interest, especially in remote locations. However, bandwidth constraint has been the primary bottleneck for efficient telementoring systems. This study aims to establish an efficient surgical telementoring system, where the qualified surgeon (mentor) provides real-time guidance and technical assistance for surgical procedures to the on-spot physician (surgeon). High Efficiency Video Coding (HEVC/H.265)-based video compression has shown promising results for telementoring applications. However, there is a trade-off between the bandwidth resources required for video transmission and quality of video received by the remote surgeon. In order to efficiently compress and transmit real-time surgical videos, a hybrid lossless-lossy approach is proposed where surgical incision region is coded in high quality whereas the background region is coded in low quality based on distance from the surgical incision region. For surgical incision region extraction, state-of-the-art deep learning (DL) architectures for semantic segmentation can be used. However, the computational complexity of these architectures is high resulting in large training and inference times. For telementoring systems, encoding time is crucial; therefore, very deep architectures are not suitable for surgical incision extraction. In this study, we propose a shallow convolutional neural network (S-CNN)-based segmentation approach that consists of encoder network only for surgical region extraction. The segmentation performance of S-CNN is compared with one of the state-of-the-art image segmentation networks (SegNet), and results demonstrate the effectiveness of the proposed network. The proposed telementoring system is efficient and explicitly considers the physiological nature of the human visual system to encode the video by providing good overall visual impact in the location of surgery. The results of the proposed S-CNN-based segmentation demonstrated a pixel accuracy of 97% and a mean intersection over union accuracy of 79%. Similarly, HEVC experimental results showed that the proposed surgical region-based encoding scheme achieved an average bitrate reduction of 88.8% at high-quality settings in comparison with default full-frame HEVC encoding. The average gain in encoding performance (signal-to-noise) of the proposed algorithm is 11.5 dB in the surgical region. The bitrate saving and visual quality of the proposed optimal bit allocation scheme are compared with the mean shift segmentation-based coding scheme for fair comparison. The results show that the proposed scheme maintains high visual quality in surgical incision region along with achieving good bitrate saving. Based on comparison and results, the proposed encoding algorithm can be considered as an efficient and effective solution for surgical telementoring systems for low-bandwidth networks.