Generative AI systems like foundation models (FMs) must align well with human values to ensure their behavior is helpful and trustworthy. While Reinforcement Learning from Human Feedback (RLHF) has shown promise for optimizing model performance using human judgments, existing RLHF pipelines predominantly rely on immediate feedback, which can fail to reflect the true downstream impact of an interaction on users' utility. We demonstrate that this shortsighted feedback can, by itself, result in misaligned behaviors like sycophancy and deception, and we propose to alleviate this by refocusing RLHF on downstream consequences. Our theoretical analysis reveals that the hindsight gained by simply delaying human feedback mitigates misalignment and improves expected human utility. To leverage this insight in a practical alignment algorithm, we introduce Reinforcement Learning from Hindsight Simulation (RLHS), which first simulates plausible consequences and then elicits feedback to assess what behaviors were genuinely beneficial in hindsight. We apply RLHS to two widely-employed online and offline preference optimization methods---Proximal Policy Optimization (PPO) and Direct Preference Optimization (DPO)---and show empirically that misalignment is significantly reduced with both methods. Through an online human user study, we show that RLHS consistently outperforms RLHF in helping users achieve their goals and earns higher satisfaction ratings, despite being trained solely with simulated hindsight feedback. These results underscore the importance of focusing on long-term consequences, even simulated ones, to mitigate misalignment in RLHF.