To meet the security and stability requirements of new power systems with high shares of renewable energy, it is essential to enhance system flexibility. Large-scale flexible loads can be aggregated and optimized by load aggregators (LAs) to participate in demand response (DR) markets and provide substantial regulation capacity. However, the response precision of LAs is not fully considered during market clearing, hindering the power system from effectively identifying high-quality flexible DR resources and failing to incentivize aggregators to improve their precision. To address this issue, this paper proposes a performance evaluation and market clearing method for LAs with an emphasis on precision regulation, aimed at enabling power systems to select high-quality DR resources. First, based on the deviations of LAs, a comprehensive response precision index that considers both short-term and long-term impacts is established to assess LAs’ performance. Then, the comprehensive index is integrated into the market clearing method and price mechanism to prioritize aggregators with higher response precision in the clearing process. Finally, case studies are conducted to validate the effectiveness of the proposed method, demonstrating that LAs with high-quality performance gain a competitive edge in future market clearings, while simultaneously reducing the overall costs of the power system to achieve precise load regulation.