Background and objectives: Spectral Domain Optical Coherence Tomography (SD-OCT) is a volumetric imaging technique that allows measuring patterns between layers such as small amounts of fluid. Since 2012, automatic medical image analysis performance has steadily increased through the use of deep learning models that automatically learn relevant features for specific tasks, instead of designing visual features manually. Nevertheless, providing insights and interpretation of the predictions made by the model is still a challenge. This paper describes a deep learning model able to detect medically interpretable information in relevant images from a volume to classify diabetes-related retinal diseases. Methods: This article presents a new deep learning model, OCT-NET, which is a customized convolutional neural network for processing scans extracted from optical coherence tomography volumes. OCT-NET is applied to the classification of three conditions seen in SD-OCT volumes. Additionally, the proposed model includes a feedback stage that highlights the areas of the scans to support the interpretation of the results. This information is potentially useful for a medical specialist while assessing the prediction produced by the model. Results: The proposed model was tested on the public SERI-CUHK and A2A SD-OCT data sets containing healthy, diabetic retinopathy, diabetic macular edema and age-related macular degeneration. The experimental evaluation shows that the proposed method outperforms conventional convolutional deep learning models from the state of the art reported on the SERI+CUHK and A2A SD-OCT data sets with a precision of 93% and an area under the ROC curve (AUC) of 0.99 respectively. Conclusions: The proposed method is able to classify the three studied retinal diseases with high accuracy. One advantage of the method is its ability to produce interpretable clinical information in the form of highlighting the regions of the image that most contribute to the classifier decision.