The performance of neural anti-spoofing models has rapidly improved in recent years due to larger network architectures and better training methodologies. However, these systems require considerable training data for achieving high performance, which makes it challenging to train them in compute-restricted environments. To make these systems accessible in resource-constrained environments, we consider the task of training neural anti-spoofing models with limited training data. We apply multiple dataset pruning techniques to the ASVspoof 2019 dataset for selecting the most informative training examples and pruning a significant chunk of the data with minimal decrease in performance. We find that the existing pruning metrics are not simultaneously granular and stable. To address this problem and further improve the performance of anti-spoofing models on pruned data, we propose a new metric, Forgetting Norm, to score individual training examples with higher granularity. Extensive experiments on two anti-spoofing models, AASIST-L and RawNet2, and several pruning settings demonstrate up to 23% relative improvement with forgetting norm over other baseline pruning heuristics. We also demonstrate the desirable properties of the proposed metric by analyzing the training landscape of the neural anti-spoofing models.