This paper presents a novel supervised convolutional neural network architecture, “DUCK-Net”, capable of effectively learning and generalizing from small amounts of medical images to perform accurate segmentation tasks. Our model utilizes an encoder-decoder structure with a residual downsampling mechanism and a custom convolutional block to capture and process image information at multiple resolutions in the encoder segment. We employ data augmentation techniques to enrich the training set, thus increasing our model's performance. While our architecture is versatile and applicable to various segmentation tasks, in this study, we demonstrate its capabilities specifically for polyp segmentation in colonoscopy images. We evaluate the performance of our method on several popular benchmark datasets for polyp segmentation, Kvasir-SEG, CVC-ClinicDB, CVC-ColonDB, and ETIS-LARIBPOLYPDB showing that it achieves state-of-the-art results in terms of mean Dice coefficient, Jaccard index, Precision, Recall, and Accuracy. Our approach demonstrates strong generalization capabilities, achieving excellent performance even with limited training data.