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Assessing the degree of disease severity in biomedical images is a task similar to standard classification but constrained by an underlying structure in the label space. Such a structure reflects the monotonic relationship between different disease grades. In this paper, we propose a straightforward approach to enforce this constraint for the task of predicting Diabetic Retinopathy (DR) severity from eye fundus images based on the well-known notion of Cost-Sensitive classification. We expand standard classification losses with an extra term that acts as a regularizer, imposing greater penalties on predicted grades when they are farther away from the true grade associated to a particular image. Furthermore, we show how to adapt our method to the modelling of label noise in each of the sub-problems associated to DR grading, an approach we refer to as Atomic Sub-Task modeling. This yields models that can implicitly take into account the inherent noise present in DR grade annotations. Our experimental analysis on several public datasets reveals that, when a standard Convolutional Neural Network is trained using this simple strategy, improvements of 3-5\% of quadratic-weighted kappa scores can be achieved at a negligible computational cost. Code to reproduce our results is released at https://github.com/agaldran/cost_sensitive_loss_classification.