Multi-class colorectal tissue classification is a challenging problem that is typically addressed in a setting, where it is assumed that ample amounts of training data is available. However, manual annotation of fine-grained colorectal tissue samples of multiple classes, especially the rare ones like stromal tumor and anal cancer is laborious and expensive. To address this, we propose a knowledge distillation-based approach, named KD-CTCNet, that effectively captures local texture information from few tissue samples, through a distillation loss, to improve the standard CNN features. The resulting enriched feature representation achieves improved classification performance specifically in low data regimes. Extensive experiments on two public datasets of colorectal tissues reveal the merits of the proposed contributions, with a consistent gain achieved over different approaches across low data settings. The code and models are publicly available on GitHub.