Generative artificial intelligence is playing a significant role in the transformation of digital ecosystems by reinventing the processes of content generation, process automation, product innovation and customer experience. At the same time that these technologies are becoming more integrated into routine operations, the focus has shifted to the ethical and environmental consequences associated with their widespread application. An investigation of the operational sustainability associated with the generative artificial intelligence systems would be crucial, as it would provide information about how these systems match ideals such as efficiency, circularity and environmental responsibility. We explore how users understand and engage with sustainability principles, specifically lean, circular and green operational frameworks within generative artificial intelligence environments. We collect user reviews of 72 recently launched generative AI platforms from 2022 to 2024 and utilise advanced machine learning methods, including Word2Vec modelling, sentiment and regression analysis, to reveal how text datasets reflect customer perceptions. We find that the lean theme is the most prominent feature of operational sustainability, with the highest sentiment score, followed by the green and circular themes. Our findings show that there is a growing respect among the general public for artificial intelligence systems that exhibit responsible and efficient design.