Automating retinal vessel segmentation is a primary element of computer-aided diagnostic systems for many retinal diseases. It facilitates the inspection of shape, width, tortuosity, and other blood vessel characteristics. In this paper, a new method that incorporates Distorted Gaussian Matched Filters (D-GMFs) with adaptive parameters as part of a Deep Convolutional Architecture is proposed. The D-GaussianNet includes D-GMF units, a variant of the Gaussian Matched Filter that considers curvature, placed at the beginning and end of the network to implicitly indicate that spatial attention should focus on curvilinear structures in the image. Experimental results on datasets DRIVE, STARE, and CHASE show state-of-the-art performance with an accuracy of 0.9565, 0.9647, and 0.9609 and a F1-score of 0.8233, 0.8141, and 0.8077, respectively.