It is critical for the proper segmentation of blood vessels in retinal images that for the early diagnosis and continuous monitoring of many retinal diseases, including diabetic retinopathy, glaucoma, and age-related macular degeneration. The paper introduces a novel approach that combines the strengths of architectures in deep learning with traditional machine learning techniques to boost performance in the segmentation of blood vessels in retinal images. Here, we combine the two well-known convolutional neural networks on the task of medical image segmentation, namely, U-Net and SegNet, with a logistic regression classifier at the end. Due to the symmetric architecture of the U-Net model, it catches complex vessel structures and fine details very well. The feature extraction capability of the SegNet model is good, and it uses the encoder-decoder framework. Using both models sequentially gives initial segmentation outputs. Fine tuning is performed with logistic regression in order to provide a more accurate and consistent output. Basically, it is a hybrid approach towards overcoming problems in blood vessel segmentation attributed to size variation of the vessel, contrast, and intensity levels in retinal images. Our approach was trained and tested on standard datasets of retinal images, and manifested the superiority of segmentation accuracy and the generalization ability. The results obtained with the final accuracy of 0.97021 outline the advantage in combining deep learning models with traditional machine learning classifiers to contribute not only to more precise segmentation but also to improved reliability of medical image analysis automated diagnostic systems, which opens further possibilities for real-world applications in retinal disease detection and management.