Rapid and accurate damage assessment following natural disasters is critical for effective emergency response. However, identifying fine-grained damage levels (e.g., distinguishing minor from major roof damage) in UAV imagery remains challenging due to the degradation of texture cues during resizing and extreme class imbalance. We propose DA-SegFormer, a damage-aware adaptation of the SegFormer architecture optimized for high-resolution disaster imagery. Our method introduces a Class-Aware Sampling strategy to guarantee exposure to rare damage features, and it integrates Online Hard Example Mining (OHEM) with Dice Loss to dynamically focus on underrepresented classes. In addition, we employ a resolution-preserving inference protocol that maintains native texture details. Evaluated on the RescueNet dataset, DA-SegFormer achieves 74.61\% mIoU, outperforming the baseline by 2.55\%. Notably, our improvements yield double-digit gains in critical damage classes: Minor Damage (+11.7%) and Major Damage (+21.3%).