The evolution of electricity markets has led to increasingly complex energy trading dynamics and the integration of renewable energy sources as well as the influence of several external market factors contributed towards price volatility. Therefore, day-ahead electricity price forecasting models, typically using some kind of neural network, play a crucial role in the optimal behavior of market agents. The most prominent models and benchmarks rely on improving the accuracy of predictions and the time for convergence by some sort of a priori processing of the dataset that is used for the training of the neural network, such as hyperparameter tuning and feature selection techniques. What has been overlooked so far is the possible benefit of a posteriori processing, which would consider the effects of parameters that could refine the predictions once they have been made. Such a parameter is the estimation of the residual training error. In this study, we investigate the effect of residual training error estimation for the day-ahead price forecasting task and propose an error compensation deep neural network model (ERC−DNN) that focuses on the minimization of prediction error, while reinforcing error stability through the integration of an autoregression module. The experiments on the Nord Pool power market indicated that this approach yields improved error metrics when compared to the baseline deep learning structure in different training scenarios, and the refined predictions for each hourly sequence shared a more stable error profile. The proposed method contributes towards the development of more flexible hybrid neural network models and the potential integration of the error estimation module in future benchmarks, given a small and interpretable set of hyperparameters.