Glaucoma is a major cause of blindness worldwide, and its early detection is essential for the timely management of the condition. Glaucoma-induced anomalies of the optic nerve head may cause variation in the Optic Disc (OD) size. Therefore, robust OD segmentation techniques are necessary for the screening for glaucoma. Computer-aided segmentation has become a promising diagnostic tool for the early detection of glaucoma, and there has been much interest in recent years in using neural networks for medical image segmentation. This study proposed an enhanced lightweight U-Net model with an Attention Gate (AG) to segment OD images. We also used a transfer learning strategy to extract relevant features using a pre-trained EfficientNet-B0 CNN, which preserved the receptive field size and AG, which reduced the impact of gradient vanishing and overfitting. Additionally, the neural network trained using the binary focal loss function improved segmentation accuracy. The pre-trained Attention U-Net was validated using publicly available datasets, such as DRIONS-DB, DRISHTI-GS, and MESSIDOR. The model significantly reduced parameter quantity by around 0.53 M and had inference times of 40.3 ms, 44.2 ms, and 60.6 ms, respectively.