Dexterous manipulation presents substantial challenges for imitation learning due to its high-dimensional action space and complex contact-rich dynamics. Policies trained purely from demonstrations often suffer from compounding errors during deployment and require large amounts of expert data to achieve reliable performance. To move beyond the limitations of demonstration data, in this work, we propose DexPIE, a post-training framework for dexterous policy improvement from experience collected through real-world deployment. First, DexPIE enables effective exploration coverage through a dexterous-hand-adapted intervention system and multi-stage DAgger-style data collection across initial and intermediate task stages, providing reliable supervision for accurate policy evaluation. To reduce temporal noise between post-training rollouts and demonstration data, we introduce asynchronous inference in the relative action space, which better aligns rollout data with demonstrated behavior and allows the critic to learn a value function induced by a more consistent underlying policy. Finally, DexPIE improves the policy through conditioning on a continuous optimality indicator, allowing the policy to leverage the quality of data in a more fine-grained manner. Across three challenging real-world dexterous manipulation tasks, DexPIE achieves a 37% improvement in success rate over the demonstration-based reference policy, outperforming all baseline methods and demonstrating stronger robustness. The source code and dataset will be made publicly available.