The molecular heterogeneity of cancer cells contributes to the often partial response to targeted therapies and relapse of disease due to the escape of resistant cell populations. While single-cell sequencing has started to improve our understanding of this heterogeneity, it offers a mostly descriptive view on cellular types and states. To obtain more functional insights, we propose scGeneRAI, an explainable deep learning approach that uses layer-wise relevance propagation (LRP) to infer gene regulatory networks from static single-cell RNA sequencing data for individual cells. We benchmark our method with synthetic data and apply it to single-cell RNA sequencing data of a cohort of human lung cancers. From the predicted single-cell networks our approach reveals characteristic network patterns for tumor cells and normal epithelial cells and identifies subnetworks that are observed only in (subgroups of) tumor cells of certain patients. While current state-of-the-art methods are limited by their ability to only predict average networks for cell populations, our approach facilitates the reconstruction of networks down to the level of single cells which can be utilized to characterize the heterogeneity of gene regulation within and across tumors.