Artificial intelligence has begun to permeate managerial decision-making, yet many organizations remain hesitant to rely on algorithms when choices carry significant consequences. To clarify the roots of this hesitation, we conducted a systematic review of 37 peer-reviewed studies published between 1970 and 2024, following the PRISMA-2020 protocol. The evidence was organized into seven interrelated themes spanning technical design, organizational structures, ethical safeguards, and the psychological climate in which managers operate. Results reveal that adoption is driven less by raw performance claims than by the degree of trust managers place in AI tools. That trust rests on three pillars: transparent and reliable system behavior, a clear perception of usefulness and ease of use, and explicit protections against bias. When any pillar is weak, anxiety about ceding control grows, dampening adoption intentions. Drawing these strands together, we propose an integrative framework that pairs cost-efficient, explainable architectures with user-centered training and governance mechanisms. The framework not only lowers technical barriers but also addresses the human and ethical concerns that most often stall implementation. By illuminating how technological, organizational, and psychological factors interact, the study offers a pragmatic roadmap for managers seeking to harness AI while safeguarding stakeholder confidence.