Concurrent to the rapid progress in the development of neural-network based models in areas like natural language processing and computer vision, the need for creating explanations for the predictions of these black-box models has risen steadily. We propose a new method to generate extractive explanations for predictions made by neural networks, that is based on masking parts of the input which the model does not consider to be indicative of the respective class. The masking is done using gradient-based optimization combined with a new regularization scheme that enforces sufficiency, comprehensiveness and compactness of the generated explanation, three properties that are known to be desirable from the related field of rationale extraction in natural language processing. In this way, we bridge the gap between model interpretability and rationale extraction, thereby proving that the latter of which can be performed without training a specialized model, only on the basis of a trained classifier. We further apply the same method to image inputs and obtain high quality explanations for image classifications, which indicates that the conditions proposed for rationale extraction in natural language processing are more broadly applicable to different input types.