Segmentation of cardiac anatomical structures in cardiac magnetic resonance images (CMRI) is a prerequisite for automatic diagnosis and prognosis of cardiovascular diseases. To increase robustness and performance of segmentation methods this study combines automatic segmentation and assessment of segmentation uncertainty in CMRI to detect image regions containing local segmentation failures. Three existing state-of-the-art convolutional neural networks (CNN) were trained to automatically segment cardiac anatomical structures and obtain two measures of predictive uncertainty: entropy and a measure derived by MC-dropout. Thereafter, using the uncertainties another CNN was trained to detect local segmentation failures that potentially need correction by an expert. Finally, manual correction of the detected regions was simulated in the complete set of scans of 100 patients and manually performed in a random subset of scans of 50 patients. Using publicly available CMR scans from the MICCAI 2017 ACDC challenge, the impact of CNN architecture and loss function for segmentation, and the uncertainty measure was investigated. Performance was evaluated using the Dice coefficient, 3D Hausdorff distance and clinical metrics between manual and (corrected) automatic segmentation. The experiments reveal that combining automatic segmentation with manual correction of detected segmentation failures results in improved segmentation and to 10-fold reduction of expert time compared to manual expert segmentation.