Despite the growing popularity of modern machine learning techniques (e.g. Deep Neural Networks) in cyber-security applications, most of these models are perceived as a black-box for the user. Adversarial machine learning offers an approach to increase our understanding of these models. In this paper we present an approach to generate explanations for incorrect classifications made by data-driven Intrusion Detection Systems (IDSs). An adversarial approach is used to find the minimum modifications (of the input features) required to correctly classify a given set of misclassified samples. The magnitude of such modifications is used to visualize the most relevant features that explain the reason for the misclassification. The presented methodology generated satisfactory explanations that describe the reasoning behind the mis-classifications, with descriptions that match expert knowledge. The advantages of the presented methodology are: 1) applicable to any classifier with defined gradients. 2) does not require any modification of the classifier model. 3) can be extended to perform further diagnosis (e.g. vulnerability assessment) and gain further understanding of the system. Experimental evaluation was conducted on the NSL-KDD99 benchmark dataset using Linear and Multilayer perceptron classifiers. The results are shown using intuitive visualizations in order to improve the interpretability of the results.