The analysis of fundus images for the early screening of eye diseases is of great clinical importance. Traditional methods for such analysis are time-consuming and expensive as they require a trained clinician. Therefore, the need for a comprehensive and automated clinical decision support system to diagnose and grade retinal diseases has long been recognized. In the past decade, with the substantial developments in computer vision and deep learning, machine learning methods have become highly effective in this field to address this need. However, most of these algorithms face challenges like computational feasibility, reliability, and interpretability. In this paper, our contributions are two-fold. First, we introduce a very powerful feature extraction method for fundus images by employing the latest topological data analysis methods. Through our experiments, we observe that our topological feature vectors are highly effective in distinguishing normal and abnormal classes for the most common retinal diseases, i.e., Diabetic Retinopathy (DR), Glaucoma, and Age-related Macular Degeneration (AMD). Furthermore, these topological features are interpretable, computationally feasible, and can be seamlessly integrated into any forthcoming ML model in the domain. Secondly, we move forward in this direction, constructing a topological deep learning model by integrating our topological features with several deep learning models. Empirical analysis shows a notable enhancement in performance aided by the use of topological features. Remarkably, our model surpasses all existing models, demonstrating superior performance across several benchmark datasets pertaining to two of these three retinal diseases.