Accurate segmentation of thin structures is critical for microsurgical scene understanding but remains challenging due to resolution loss, low contrast, and class imbalance. We propose Microsurgery Instrument Segmentation for Robotic Assistance(MISRA), a segmentation framework that augments RGB input with luminance channels, integrates skip attention to preserve elongated features, and employs an Iterative Feedback Module(IFM) for continuity restoration across multiple passes. In addition, we introduce a dedicated microsurgical dataset with fine-grained annotations of surgical instruments including thin objects, providing a benchmark for robust evaluation Dataset available at https://huggingface.co/datasets/KIST-HARILAB/MISAW-Seg. Experiments demonstrate that MISRA achieves competitive performance, improving the mean class IoU by 5.37% over competing methods, while delivering more stable predictions at instrument contacts and overlaps. These results position MISRA as a promising step toward reliable scene parsing for computer-assisted and robotic microsurgery.