Diabetic retinopathy (DR) is a medical condition due to diabetes mellitus that can damage the patient retina and cause blood leaks. This condition can cause different symptoms from mild vision problems to complete blindness if it is not timely treated. In this work, we propose the use of a deep learning architecture based on a recent convolutional neural network called EfficientNet to detect referable diabetic retinopathy (RDR) and vision-threatening DR. Tests were conducted on two public datasets, EyePACS and APTOS 2019. The obtained results achieve state-of-the-art performance and show that the proposed network leads to higher classification rates, achieving an Area Under Curve (AUC) of 0.984 for RDR and 0.990 for vision-threatening DR on EyePACS dataset. Similar performances are obtained for APTOS 2019 dataset with an AUC of 0.966 and 0.998 for referable and vision-threatening DR, respectively. An explainability algorithm was also developed and shows the efficiency of the proposed approach in detecting DR signs.