Music classification has been one of the most popular tasks in the field of music information retrieval. With the development of deep learning models, the last decade has seen impressive improvements in a wide range of classification tasks. However, the increasing model complexity makes both training and inference computationally expensive. In this paper, we integrate the ideas of transfer learning and feature-based knowledge distillation and systematically investigate using pre-trained audio embeddings as teachers to guide the training of low-complexity student networks. By regularizing the feature space of the student networks with the pre-trained embeddings, the knowledge in the teacher embeddings can be transferred to the students. We use various pre-trained audio embeddings and test the effectiveness of the method on the tasks of musical instrument classification and music auto-tagging. Results show that our method significantly improves the results in comparison to the identical model trained without the teacher's knowledge. This technique can also be combined with classical knowledge distillation approaches to further improve the model's performance.