Deep Learning has become a very valuable tool in different fields, and no one doubts the learning capacity of these models. Nevertheless, since Deep Learning models are often seen as black boxes due to their lack of interpretability, there is a general mistrust in their decision-making process. To find a balance between effectiveness and interpretability, Explainable Artificial Intelligence (XAI) is gaining popularity in recent years, and some of the methods within this area are used to generate counterfactual explanations. The process of generating these explanations generally consists of solving an optimization problem for each input to be explained, which is unfeasible when real-time feedback is needed. To speed up this process, some methods have made use of autoencoders to generate instant counterfactual explanations. Recently, a method called Deep Guided Counterfactual Explanations (DGCEx) has been proposed, which trains an autoencoder attached to a classification model, in order to generate straightforward counterfactual explanations. However, this method does not ensure that the generated counterfactual instances are close to the data manifold, so unrealistic counterfactual instances may be generated. To overcome this issue, this paper presents Distribution Aware Deep Guided Counterfactual Explanations (DA-DGCEx), which adds a term to the DGCEx cost function that penalizes out of distribution counterfactual instances.