Gene Regulatory Network (GRN) inference is essential for understanding complex cellular mechanisms, rendered tractable through single-cell transcriptomic data. With the emergence of single-cell Foundation Models (scFMs), enhanced transcriptomic encoding is widely expected to revolutionize GRN inference. However, we observe that their performance remains far from satisfactory. The primary reason is that the standard reconstruction-based pre-training objectives often fail to explicitly capture latent regulatory signals. To bridge this gap, we first introduce a GRN generalization benchmark designed to evaluate regulatory predictions on unseen genes and datasets, which relies on the zero-shot capabilities of scFMs and is inherently challenging for traditional methods. Furthermore, to unlock the regulatory knowledge within the foundation models, we propose two novel methods, Virtual Value Perturbation and Gradient Trajectory, to distill implicit regulatory information from scFMs into highly generalizable inter-gene features. Extensive experiments demonstrate that our approach significantly outperforms existing methods, establishing a new paradigm for leveraging the potential of scFMs in universal GRN inference.