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In the rapidly advancing domain of artificial intelligence applied to materials science, systems are frequently called upon to make critical decisions under conditions of substantial uncertainty, such as selecting which candidate material to synthesize next, which experiment to prioritize for evaluation, or which property to measure in a given campaign. A fundamental aspect that current materials AI approaches largely ignore is the phenomenon of regret—the realization, after the fact, that a different choice would have produced a superior outcome, often carrying emotional, cognitive, and practical costs for the decision-maker. Regret theory, originating in decision theory and economics, provides a powerful alternative lens for understanding choice under uncertainty by incorporating not only expected utilities but also the anticipation and experience of post-decision disappointment or rejoicing. This paper proposes a conceptual framework for regret-aware materials AI systems that explicitly integrates regret quantification, theoretical regret bounds, regret minimization objectives, regret-aware acquisition functions, and regret communication mechanisms into the decision-making pipeline. The framework further delineates four primary types of regret encountered in materials contexts—synthesis regret, measurement regret, discovery regret, and resource regret—each arising from the irreversible, sequential, and high-stakes nature of experimental materials research. By embedding these elements, the proposed framework shifts materials AI from a narrow focus on reward maximization toward systems that more closely mirror the nuanced realities of scientific decision-making, where the avoidance of avoidable regret becomes a central design goal. Ultimately, embracing regret awareness promises more robust exploration of vast material spaces, better alignment between AI recommendations and laboratory constraints, and enhanced trust between human researchers and autonomous systems, thereby accelerating genuine discovery while mitigating the hidden costs of overlooked alternatives.