Event extraction aims to identify triggers in text, classify them into predefined event types, and recognize associated arguments such as participants and locations. Large language model (LLM)-based generative approaches provide a unified paradigm for joint trigger identification, classification, and argument extraction; however, their computational cost necessitates knowledge distillation (KD) into smaller student models. Existing KD methods operate at the token level, treating each output position independently and thus failing to concentrate the distillation signal on event-relevant spans or to capture the relational structure among event components. We propose EventKD, a two-level distillation framework tailored for event extraction. At the token level, a distributional divergence loss incorporates event-aware span importance weighting to prioritize tokens corresponding to triggers, arguments, and type labels. At the span level, a Relational-Aware (RA) loss preserves pairwise geometric relationships among event-aware spans across Transformer layers. Experiments on four benchmarks (ACE05, MAVEN, GENEVA, and RAMS) demonstrate that EventKD consistently outperforms existing distillation methods on both trigger identification and argument extraction.