Three-dimensional (3D)-image-based anatomical analysis of rotator cuff tear patients has been proposed as a way to improve repair prognosis analysis to reduce the incidence of postoperative retear. However, for application in clinics, an efficient and robust method for the segmentation of anatomy from MRI is required. We present the use of a deep learning network for automatic segmentation of the humerus, scapula, and rotator cuff muscles with integrated automatic result verification. Trained on N = 111 and tested on N = 60 diagnostic T1-weighted MRI of 76 rotator cuff tear patients acquired from 19 centers, a nnU-Net segmented the anatomy with an average Dice coefficient of 0.91 ± 0.06. For the automatic identification of inaccurate segmentations during the inference procedure, the nnU-Net framework was adapted to allow for the estimation of label-specific network uncertainty directly from its subnetworks. The average Dice coefficient of segmentation results from the subnetworks identified labels requiring segmentation correction with an average sensitivity of 1.0 and a specificity of 0.94. The presented automatic methods facilitate the use of 3D diagnosis in clinical routine by eliminating the need for time-consuming manual segmentation and slice-by-slice segmentation verification.