Deep Neural Networks are often brittle on image classification tasks and known to misclassify inputs. While these misclassifications may be inevitable, all failure modes cannot be considered equal. Certain misclassifications (eg. classifying the image of a dog to an airplane) can perplex humans and result in the loss of human trust in the system. Even worse, these errors (eg. a person misclassified as a primate) can have odious societal impacts. Thus, in this work, we aim to reduce inexplicable errors. To address this challenge, we first discuss methods to obtain the class-level semantics that capture the human's expectation ($M^h$) regarding which classes are semantically close {\em vs.} ones that are far away. We show that for popular image benchmarks (like CIFAR-10, CIFAR-100, ImageNet), class-level semantics can be readily obtained by leveraging either human subject studies or publicly available human-curated knowledge bases. Second, we propose the use of Weighted Loss Functions (WLFs) to penalize misclassifications by the weight of their inexplicability. Finally, we show that training (or fine-tuning) existing classifiers with the proposed methods lead to Deep Neural Networks that have (1) comparable top-1 accuracy, (2) more explicable failure modes on both in-distribution and out-of-distribution (OOD) test data, and (3) incur significantly less cost in the gathering of additional human labels compared to existing works.