Rapid and accurate post-hurricane damage assessment is vital for disaster response and recovery. Yet existing CNN-based methods struggle to capture multi-scale spatial features and to distinguish visually similar or co-occurring damage types. To address these issues, we propose MCANet, a multi-label classification framework that learns multi-scale representations and adaptively attends to spatially relevant regions for each damage category. MCANet employs a Res2Net-based hierarchical backbone to enrich spatial context across scales and a multi-head class-specific residual attention module to enhance discrimination. Each attention branch focuses on different spatial granularities, balancing local detail with global context. We evaluate MCANet on the RescueNet dataset of 4,494 UAV images collected after Hurricane Michael. MCANet achieves a mean average precision (mAP) of 91.75%, outperforming ResNet, Res2Net, VGG, MobileNet, EfficientNet, and ViT. With eight attention heads, performance further improves to 92.35%, boosting average precision for challenging classes such as Road Blocked by over 6%. Class activation mapping confirms MCANet's ability to localize damage-relevant regions, supporting interpretability. Outputs from MCANet can inform post-disaster risk mapping, emergency routing, and digital twin-based disaster response. Future work could integrate disaster-specific knowledge graphs and multimodal large language models to improve adaptability to unseen disasters and enrich semantic understanding for real-world decision-making.