In proteomic analysis pipelines, machine learning post-processors play a critical role in improving the accuracy of shotgun proteomics analysis. Most often performed in a semi-supervised manner, such post-processors accept the peptide-spectrum matches (PSMs) and corresponding feature vectors resulting from a database search, train a machine learning classifier, and recalibrate PSM scores based on the resulting trained parameters, often leading to significantly more identified peptides across q-value thresholds. However, current state-of-the-art post-processors rely on shallow machine learning methods, such as SVMs, gradient boosted decision trees, and linear discriminant analysis. In contrast, the powerful learning capabilities of deep models have displayed superior performance to shallow models in an ever-growing number of other fields. In this work, we show that deep neural networks (DNNs) significantly improve the recalibration of shotgun proteomics data compared to the most accurate and widely used post-processors, such as Percolator and PeptideProphet. Furthermore, we show that DNNs are able to adaptively analyze complex datasets and features for more accurate universal post-processing, leading to both improved Prosit analysis and markedly better recalibration of recently developed p-value scoring functions.