Visual explanation methods have an important role in the prognosis of the patients where the annotated data is limited or not available. There have been several attempts to use gradient-based attribution methods to localize pathology from medical scans without using segmentation labels. This research direction has been impeded by the lack of robustness and reliability. These methods are highly sensitive to the network parameters. In this study, we introduce a robust visual explanation method to address this problem for medical applications. We provide a highly innovative algorithm to quantifying lesions in the lungs caused by the Covid-19 with high accuracy and robustness without using dense segmentation labels. Inspired by the information bottleneck concept, we mask the neural network representation with noise to find out important regions. This approach overcomes the drawbacks of commonly used Grad-Cam and its derived algorithms. The premise behind our proposed strategy is that the information flow is minimized while ensuring the classifier prediction stays similar. Our findings indicate that the bottleneck condition provides a more stable and robust severity estimation than the similar attribution methods.