As emotional states are diverse, simply classifying them through discrete facial expressions has its limitations. Therefore, to create a facial expression recognition system for practical applications, not only must facial expressions be classified, emotional changes must be measured as continuous values. Based on the knowledge distillation structure and the teacher-bounded loss function, we propose a method to maximize the synergistic effect of jointly learning discrete and continuous emotional states of eight expression classes, valences, and arousal levels. The proposed knowledge distillation model uses Emonet, a state-of-the-art continuous estimation method, as the teacher model, and uses a lightweight network as the student model. It was confirmed that performance degradation can be minimized even though student models have multiply-accumulate operations of approximately 3.9 G and 0.3 G when using EfficientFormer and MobileNetV2, respectively, which is much less than the amount of computation required by the teacher model (16.99 G). Together with the significant improvements in computational efficiency (by 4.35 and 56.63 times using EfficientFormer and MobileNetV2, respectively), the decreases in facial expression classification accuracy were approximately 1.35% and 1.64%, respectively. Therefore, the proposed method is optimized for application-level interaction systems in terms of both the amount of computation required and the accuracy.