Chest computed tomography (CT) imaging has become indispensable for staging and managing coronavirus disease 2019 (COVID-19), and current evaluation of anomalies/abnormalities associated with COVID-19 has been performed majorly by the visual score. The development of automated methods for quantifying COVID-19 abnormalities in these CT images is invaluable to clinicians. The hallmark of COVID-19 in chest CT images is the presence of ground-glass opacities in the lung region, which are tedious to segment manually. We propose anamorphic depth embedding-based lightweight CNN, called Anam-Net, to segment anomalies in COVID-19 chest CT images. The proposed Anam-Net has 7.8 times fewer parameters compared to the state-of-the-art UNet (or its variants), making it lightweight capable of providing inferences in mobile or resource constraint (point-of-care) platforms. The results from chest CT images (test cases) across different experiments showed that the proposed method could provide good Dice similarity scores for abnormal and normal regions in the lung. We have benchmarked Anam-Net with other state-of-the-art architectures, such as ENet, LEDNet, UNet++, SegNet, Attention UNet, and DeepLabV3+. The proposed Anam-Net was also deployed on embedded systems, such as Raspberry Pi 4, NVIDIA Jetson Xavier, and mobile-based Android application (CovSeg) embedded with Anam-Net to demonstrate its suitability for point-of-care platforms. The generated codes, models, and the mobile application are available for enthusiastic users at https://github.com/NaveenPaluru/Segmentation-COVID-19.