Segmentation of Hypoxic-Ischemic Encephalopathy (HIE) lesions in neonatal MRI is a crucial but challenging task due to diffuse multifocal lesions with varying volumes and the limited availability of annotated HIE lesion datasets. With data and label scarcity, the choice of the most appropriate loss for the pixel-level segmentation problem becomes more important. we evaluated various loss functions, including Dice, Dice-Focal, Tversky, Hausdorff Distance (HausdorffDT) Loss, and two proposed compound losses—Dice-Focal-HausdorffDT and Tversky-HausdorffDT—to enhance segmentation performance. The results show that different loss functions predict distinct segmentation masks, with compound losses outperforming standalone losses. Tversky-HausdorffDT Loss achieves the highest Dice and Normalized Surface Dice scores, while Dice-Focal-HausdorffDT Loss minimizes Mean Surface Distance. This work demonstrates the significance of task-specific loss function optimization, demonstrating that combining region-based and boundary-aware losses leads to more accurate HIE lesion segmentation, even with limited training data.