Identification of retinal diseases in automated screening methods, such as those used in clinical settings or computer-aided diagnosis, usually depends on the localization and segmentation of the Optic Disc (OD) and fovea. However, this task is difficult since these anatomical features have irregular spatial, texture, and shape characteristics, limited sample sizes, and domain shifts due to different data distributions across datasets. This study proposes a novel Multiresolution Cascaded Attention U-Net (MCAU-Net) model that addresses these problems by optimally balancing receptive field size and computational efficiency. The MCAU-Net utilizes two skip connections to accurately localize and segment the OD and fovea in fundus images. We incorporated a Multiresolution Wavelet Pooling Module (MWPM) into the CNN at each stage of U-Net input to compensate for spatial information loss. Additionally, we integrated a cascaded connection of the spatial and channel attentions as a skip connection in MCAU-Net to concentrate precisely on the target object and improve model convergence for segmenting and localizing OD and fovea centers. The proposed model has a low parameter count of 0.8 million, improving computational efficiency and reducing the risk of overfitting. For OD segmentation, the MCAU-Net achieves high IoU values of 0.9771, 0.945, and 0.946 for the DRISHTI-GS, DRIONS-DB, and IDRiD datasets, respectively, outperforming previous results for all three datasets. For the IDRiD dataset, the MCAU-Net locates the OD center with an Euclidean Distance (ED) of 16.90 pixels and the fovea center with an ED of 33.45 pixels, demonstrating its effectiveness in overcoming the common limitations of state-of-the-art methods.