This paper introduces the minimum error entropy (MEE) criterion as an advanced information-theoretic loss function tailored for deep learning applications in wireless communications. The MEE criterion leverages higher-order statistical properties, offering robustness in noisy scenarios like Rayleigh fading and impulsive interference. In addition, we propose a less computationally complex version of the MEE function to enhance practical usability in wireless communications. The method is evaluated through simulations on two critical applications: over-the-air regression and indoor localization. Results indicate that the MEE criterion outperforms conventional loss functions, such as mean squared error (MSE) and mean absolute error (MAE), achieving significant performance improvements in terms of accuracy, over $20 \%$ gain over traditional methods, and convergence speed across various channel conditions. This work establishes MEE as a promising alternative for wireless communication tasks in deep learning models, enabling better resilience and adaptability.