Gastrointestinal polyps are observed and treated under endoscopy, so there presents significant challenges to advance endoscopy imaging segmentation of polyps. Current methodologies often falter in distinguishing complex polyp structures within diverse (mucosal) tissue environments. In this paper, we propose the Frequency Attention-Embedded Network (FAENet), a novel approach leveraging frequency-based attention mechanisms to enhance polyp segmentation accuracy significantly. FAENet ingeniously segregates and processes image data into high and low-frequency components, enabling precise delineation of polyp boundaries and internal structures by integrating intra-component and cross-component attention mechanisms. This method not only preserves essential edge details but also refines the learned representation attentively, ensuring robust segmentation across varied imaging conditions. Comprehensive evaluations on two public datasets, Kvasir-SEG and CVC-ClinicDB, demonstrate FAENet's superiority over several state-of-the-art models in terms of Dice coefficient, Intersection over Union (IoU), sensitivity, and specificity. The results affirm that FAENet's advanced attention mechanisms significantly improve the segmentation quality, outperforming traditional and contemporary techniques. FAENet's success indicates its potential to revolutionize polyp segmentation in clinical practices, fostering diagnosis and efficient treatment of gastrointestinal polyps.