Developing deep learning models to analyze histology images has been computationally challenging, as the massive size of the images causes excessive strain on all parts of the computing pipeline. This paper proposes a novel deep learning-based methodology for improving the computational efficiency of histology image classification. The proposed approach is robust when used with images that have reduced input resolution, and it can be trained effectively with limited labeled data. Moreover, our approach operates at either the tissue- or slide-level, removing the need for laborious patch-level labeling. Our method uses knowledge distillation to transfer knowledge from a teacher model pre-trained at high resolution to a student model trained on the same images at a considerably lower resolution. Also, to address the lack of large-scale labeled histology image datasets, we perform the knowledge distillation in a self-supervised fashion. We evaluate our approach on three distinct histology image datasets associated with celiac disease, lung adenocarcinoma, and renal cell carcinoma. Our results on these datasets demonstrate that a combination of knowledge distillation and self-supervision allows the student model to approach and, in some cases, surpass the teacher model's classification accuracy while being much more computationally efficient. Additionally, we observe an increase in student classification performance as the size of the unlabeled dataset increases, indicating that there is potential for this method to scale further with additional unlabeled data. Our model outperforms the high-resolution teacher model for celiac disease in accuracy, F1-score, precision, and recall while requiring 4 times fewer computations. For lung adenocarcinoma, our results at 1.25× magnification are within 1.5% of the results for the teacher model at 10× magnification, with a reduction in computational cost by a factor of 64. Our model on renal cell carcinoma at 1.25× magnification performs within 1% of the teacher model at 5× magnification while requiring 16 times fewer computations. Furthermore, our celiac disease outcomes benefit from additional performance scaling with the use of more unlabeled data. In the case of 0.625× magnification, using unlabeled data improves accuracy by 4% over the tissue-level baseline. Therefore, our approach can improve the feasibility of deep learning solutions for digital pathology on standard computational hardware and infrastructures.