Glaucoma remains a leading cause of irreversible blindness worldwide and is particularly prevalent in Brazil, according to the Brazilian Society of Glaucoma (SBG). Early detection is critical to preventing vision loss. However, diagnosis in the initial stages is often challenging due to the asymptomatic nature of the disease and its visual similarities to other ophthalmic conditions. This work introduces EffAttNet (Efficient Attention Network), a novel deep learning architecture designed for automated glaucoma detection from retinal fundus images. EffAttNet leverages the representational power of EfficientNet-B3 while integrating residual attention modules to enhance feature focus and improve classification performance. Evaluated on the SMDG-19 dataset, EffAttNet achieved an accuracy of 88.27%, recall of 84.49%, and an AUC-ROC of 0.936, demonstrating its potential as a reliable tool for assisting in early glaucoma screening.