Vessel image segmentation plays a pivotal role in medical diagnostics, aiding in the early detection and treatment of vascular diseases. While segmentation based on deep learning has shown promising results, effectively segmenting small structures and maintaining connectivity between them remains challenging. To address these limitations, we propose GAEI-UNet, a novel model that combines global attention and elastic interaction-based techniques. GAEI-UNet leverages global spatial and channel context information to enhance high-level semantic understanding within the U-Net architecture, enabling precise segmentation of small vessels. Additionally, we adopt an elastic interaction-based loss function to improve connectivity among these fine structures. By capturing the forces generated by misalignment between target and predicted shapes, our model effectively learns to preserve the correct topology of vessel networks. Evaluation on retinal vessel dataset -- DRIVE demonstrates the superior performance of GAEI-UNet in terms of SE and connectivity of small structures, without significantly increasing computational complexity. This research aims to advance the field of vessel image segmentation, providing more accurate and reliable diagnostic tools for the medical community. The implementation code is available on Code.