CAREF introduces a calibration-aware regularization framework designed to improve explanation faithfulness in large language models without requiring rationale supervision. The framework is built around the novel Sparsity-Calibrated Entropic Divergence (SCED) objective, which unifies entropy calibration and adaptive token-level sparsity within a single differentiable regularization term. By encouraging predictions to rely on compact, stable, and decision-relevant token subsets, CAREF strengthens the connection between model decisions and generated explanations while maintaining strong predictive performance. Extensive evaluations on four Natural Language Explanation benchmarks demonstrate consistent improvements in both accuracy and explanation alignment, with the CAREF-AQ variant achieving state-of-the-art results using only 6.43% of trainable parameters.