Because of the pervasive use of deep neural networks (DNNs), especially in high-stakes domains, the interpretability of DNNs has received increased attention. The general idea of rationale extraction (RE) is to provide an interpretable-by-design framework for DNNs via a select-predict architecture where two neural networks learn jointly to perform feature selection and prediction, respectively. Given only the remote supervision from the final task prediction, the process of learning to select subsets of features (or rationales) requires searching in the space of all possible feature combinations, which is computationally challenging and even harder when the base neural networks are not sufficiently capable. To improve the predictive performance of RE models that are based on less capable or smaller neural networks (i.e., the students), we propose REKD (Rationale Extraction with Knowledge Distillation) where a student RE model learns from the rationales and predictions of a teacher (i.e., a rationalist) in addition to the student's own RE optimization. This structural adjustment to RE aligns well with how humans could learn effectively from interpretable and verifiable knowledge. Because of the neural-model agnostic nature of the method, any black-box neural network could be integrated as a backbone model. To demonstrate the viability of REKD, we conduct experiments with multiple variants of BERT and vision transformer (ViT) models. Our experiments across language and vision classification datasets (i.e., IMDB movie reviews, CIFAR 10 and CIFAR 100) show that REKD significantly improves the predictive performance of the student RE models.