Age-related macular degeneration (AMD) and Stargardt disease are the leading causes of blindness for the elderly and young adults respectively. Geographic atrophy (GA) of AMD and Stargardt atrophy are their end-stage outcomes. Efficient methods for segmentation and quantification of these atrophic lesions are critical for clinical research. In this study, we developed a deep convolutional neural network (CNN) with a trainable self-attended mechanism for accurate GA and Stargardt atrophy segmentation. Compared with traditional post-hoc attention mechanisms which can only visualize CNN features, our self-attended mechanism is embedded in a fully convolutional network and directly involved in training the CNN to actively attend key features for enhanced algorithm performance. We applied the self-attended CNN on the segmentation of AMD and Stargardt atrophic lesions on fundus autofluorescence (FAF) images. Compared with a preexisting regular fully convolutional network (the U-Net), our self-attended CNN achieved 10.6% higher Dice coefficient and 17% higher IoU (intersection over union) for AMD GA segmentation, and a 22% higher Dice coefficient and a 32% higher IoU for Stargardt atrophy segmentation. With longitudinal image data having over a longer time, the developed self-attended mechanism can also be applied on the visual discovery of early AMD and Stargardt features.