Configuration settings are essential for tailoring software behavior to meet specific performance requirements. However, incorrect configurations are widespread, and identifying those that impact system performance is challenging due to the vast number and complexity of possible settings. In this work, we present PerfSense, a lightweight framework that leverages Large Language Models (LLMs) to efficiently identify performance-sensitive configurations with minimal overhead. PerfSense employs LLM agents to simulate interactions between developers and performance engineers using advanced prompting techniques such as prompt chaining and retrieval-augmented generation (RAG). Our evaluation of seven open-source Java systems demonstrates that PerfSense achieves an average accuracy of 64.77% in classifying performance-sensitive configurations, outperforming both our LLM baseline (50.36%) and the previous state-of-the-art method (61.75%). Notably, our prompt chaining technique improves recall by 10% to 30% while maintaining similar precision levels. Additionally, a manual analysis of 362 misclassifications reveals common issues, including LLMs' misunderstandings of requirements (26.8%). In summary, PerfSense significantly reduces manual effort in classifying performance-sensitive configurations and offers valuable insights for future LLM-based code analysis research.