Routine inspections for critical infrastructures such as bridges are required in most jurisdictions worldwide. Such routine inspections are largely visual in nature, which are qualitative, subjective, and not repeatable. Although robotic infrastructure inspections address such limitations, they cannot replace the superior ability of experts to make decisions in complex situations, thus making human-robot interaction systems a promising technology. This study presents a novel gaze-based human-robot interaction system, designed to augment the visual inspection performance through mixed reality. Through holograms from a mixed reality device, gaze can be utilized effectively to estimate the properties of the defect in real-time. Additionally, inspectors can monitor the inspection progress on-line, which enhances the speed of the entire inspection process. Limited controlled experiments demonstrate its effectiveness across various users and defect types. To our knowledge, this is the first demonstration of the real-time application of eye gaze in civil infrastructure inspections.