Post-training of large language models is essential for adapting pre-trained language models (PLMs) to align with human preferences and downstream tasks. While PLMs typically exhibit well-calibrated confidence, post-trained language models (PoLMs) often suffer from over-confidence, assigning high confidence to both correct and incorrect outputs, which can undermine reliability in critical applications. A major obstacle in calibrating PoLMs is the scarcity of labeled data for individual downstream tasks. To address this, we propose Disagreement-Aware Confidence Alignment (DACA), a novel unsupervised method to optimize the parameters (e.g., temperature $\tau$) in post-hoc confidence calibration. Our method is motivated by the under-confidence issue caused by prediction disagreement between the PLM and PoLM while aligning their confidence via temperature scaling. Theoretically, the PLM's confidence underestimates PoLM's prediction accuracy on disagreement examples, causing a larger $\tau$ and producing under-confident predictions. DACA mitigates this by selectively using only agreement examples for calibration, effectively decoupling the influence of disagreement. In this manner, our method avoids an overly large $\tau$ in temperature scaling caused by disagreement examples, improving calibration performance. Extensive experiments demonstrate the effectiveness of our method, improving the average ECE of open-sourced and API-based LLMs (e.g. GPT-4o) by up to 15.08$\%$ on common benchmarks.