Deep learning has substantially advanced medical image segmentation, yet achieving robust generalization across diverse imaging modalities and anatomical structures remains a major challenge. A key contributor to this limitation lies in how existing architectures, ranging from CNNs to Transformers and their hybrids, primarily encode spatial information while overlooking frequency-domain representations that capture rich structural and textural cues. Although few recent studies have begun exploring spectral information at the feature level, supervision-level integration of frequency cues-crucial for fine-grained object localization-remains largely untapped. To this end, we propose Phi-SegNet, a CNN-based architecture that incorporates phase-aware information at both architectural and optimization levels. The network integrates Bi-Feature Mask Former (BFMF) modules that blend neighboring encoder features to reduce semantic gaps, and Reverse Fourier Attention (RFA) blocks that refine decoder outputs using phase-regularized features. A dedicated phase-aware loss aligns these features with structural priors, forming a closed feedback loop that emphasizes boundary precision. Evaluated on five public datasets spanning X-ray, US, histopathology, MRI, and colonoscopy, Phi-SegNet consistently achieved state-of-the-art performance, with an average relative improvement of 1.54+/-1.26% in IoU and 0.98+/-0.71% in F1-score over the next best-performing model. In cross-dataset generalization scenarios involving unseen datasets from the known domain, Phi-SegNet also exhibits robust and superior performance, highlighting its adaptability and modality-agnostic design. These findings demonstrate the potential of leveraging spectral priors in both feature representation and supervision, paving the way for generalized segmentation frameworks that excel in fine-grained object localization.