The increasing adoption of neural networks in learning-augmented systems highlights the importance of model safety and robustness, particularly in safety-critical domains. Despite progress in the formal verification of neural networks, current practices require users to manually define model specifications -- properties that dictate expected model behavior in various scenarios. This manual process, however, is prone to human error, limited in scope, and time-consuming. In this paper, we introduce AutoSpec, the first framework to automatically generate comprehensive and accurate specifications for neural networks in learning-augmented systems. We also propose the first set of metrics for assessing the accuracy and coverage of model specifications, establishing a benchmark for future comparisons. Our evaluation across four distinct applications shows that AutoSpec outperforms human-defined specifications as well as two baseline approaches introduced in this study.