Context: Human-centric software design and development focuses on how users want to carry out their tasks rather than making users accommodate their software. Software users can have different genders, ages, cultures, languages, disabilities, socioeconomic statuses, and educational backgrounds, among many other differences. Due to the inherently varied nature of these differences and their impact on software usage, preferences and issues of users can vary, resulting in user-specific defects that we term as `human-centric defects' (HCDs). Objective: This research aims to understand the perception and current management practices of such human-centric defects by software practitioners, identify key challenges in reporting, understanding and fixing them, and provide recommendations to improve HCDs management in software engineering. Method: We conducted a survey and interviews with software engineering practitioners to gauge their knowledge and experience on HCDs and the defect tracking process. Results: We analysed fifty (50) survey- and ten (10) interview- responses from SE practitioners and identified that there are multiple gaps in the current management of HCDs in software engineering practice. There is a lack of awareness regarding human-centric aspects, causing them to be lost or under-appreciated during software development. Our results revealed that handling HCDs could be improved by following a better feedback process with end-users, a more descriptive taxonomy, and suitable automation. Conclusion: HCDs present a major challenge to software practitioners, given their diverse end-user base. In the software engineering domain, research on HCDs has been limited and requires effort from the research and practice communities to create better awareness and support regarding human-centric aspects.