The rise of large-scale, sequence-based deep neural networks (DNNs) for predicting gene expression has introduced challenges in their evaluation and interpretation. Current evaluations align DNN predictions with experimental perturbation assays, which provides insights into the generalization capabilities within the studied loci but offers a limited perspective of what drives their predictions. Moreover, existing model explainability tools focus mainly on motif analysis, which becomes complex when interpreting longer sequences. Here we introduce CREME, an in silico perturbation toolkit that interrogates large-scale DNNs to uncover rules of gene regulation that it learns. Using CREME, we investigate Enformer, a prominent DNN in gene expression prediction, revealing cis-regulatory elements (CREs) that directly enhance or silence target genes. We explore the intricate complexity of higher-order CRE interactions, the relationship between CRE distance from transcription start sites on gene expression, as well as the biochemical features of enhancers and silencers learned by Enformer. Moreover, we demonstrate the flexibility of CREME to efficiently uncover a higher-resolution view of functional sequence elements within CREs. This work demonstrates how CREME can be employed to translate the powerful predictions of large-scale DNNs to study open questions in gene regulation.