The interest in the application of nonlinear methodologies for the analysis of electroencephalography signals for automatic recognition of emotions has increased notably. A vast number of studies in the research field of emotions detection have focused on the identification of the four quadrants of the valence-arousal emotional model. In this work, the recently introduced dispersion entropy (DispEn) has been applied for the first time to discern between the four groups of emotions corresponding to the four quadrants. This entropy-based index has demonstrated a considerable performance when dealing with this problem. Concretely, frontal and parieto-occipital brain regions reported the most relevant results when identifying the four emotional groups. Furthermore, the implementation of a classification model based on a sequential forward selection (SFS) approach and a support vector machine (SVM) classifier provided an average accuracy of 89.54%. This result is comparable to similar works in the scientific literature, with the advantage that the controlled selection of a reduced number of input features by means of the SFS scheme allowed to give a clinical interpretation of the outcomes. Therefore, it has been possible to reveal new insights about the performance of the most relevant brain regions involved in the processing of emotional information.