Defining the loss function is an important part of neural network design and critically determines the success of deep learning modeling. A significant shortcoming of the conventional loss functions is that they weight all regions in the input image volume equally, despite the fact that the system is known to be heterogeneous (i.e., some regions can achieve high prediction performance more easily than others). Here, we introduce a region-specific loss to lift the implicit assumption of homogeneous weighting for better learning. We divide the entire volume into multiple sub-regions, each with an individualized loss constructed for optimal local performance. Effectively, this scheme imposes higher weightings on the sub-regions that are more difficult to segment, and vice versa. Furthermore, the regional false positive and false negative errors are computed for each input image during a training step and the regional penalty is adjusted accordingly to enhance the overall accuracy of the prediction. Using different public and in-house medical image datasets, we demonstrate that the proposed regionally adaptive loss paradigm outperforms conventional methods in the multi-organ segmentations, without any modification to the neural network architecture or additional data preparation.