Recent globalization and industrialization efforts have pushed many companies to seriously consider innovation efficiency and its effectiveness. Industries seek to integrate innovation thinking in the company, resulting in different innovation theories. However, these theories become mostly ineffective when disruptions such as pandemics, political instability, or other natural events occur. In response to such disruptions, frugal innovation has been adopted in recent years because it can maximize efficiency with fewer resources. While frugal thinking is effective from an economic perspective, not enough attention has been devoted to exploring this innovative thinking method from the perspective of other pillars of sustainability (environment and society). This article focuses on this gap to deepen the understanding of sustainable frugal innovation in a recent business environment under various theoretical perspectives (triple bottom line, diffusion of innovation, and critical success factor theories). Technology is a vehicle for innovation, so this article integrates the technological advantages of AI with sustainable frugal innovation as a driving force for its effective implementation; other existing studies are limited. Integrating AI with sustainable frugal innovation requires precise actions that can be the result of understanding AIs critical success factors from the perspectives of sustainable frugal thinking. Therefore, this article analyzes the critical success factors for AI through grey DEMATEL. A research framework has been proposed and validated with a Danish case study context. Among 24 overall common critical success factors, "understanding the concept of AI" and "level of AI investment" in sustainable frugal innovation are identified as the most influential success factors. In addition, influential connections among other overall common success factors are presented. These findings could motivate industries to explore different options for successfully integrating AI with their sustainable frugal thinking, which may increase their business competitiveness during disruptions in a more sustainable way.