This study aimed to explore the impact of basic psychological needs on satisfaction with using generative AI and ChatGPT in particular. Further, an adaptation of the "Basic Psychological Need Satisfaction for Technology Use" (BPN-TU) scale was conducted throughout the study. The study developed a unique research model based on the "expectation confirmation theory" (ECT) and evaluated the research model based on data from 700 actual users. A dual approach combining "structural equation modeling" (SEM) and "artificial neural network" (ANN) techniques was utilized to analyze data. SEM results showed that basic psychological needs including autonomy, relatedness to others, and relatedness to technology significantly influence satisfaction with generative AI use. Further, perceived usefulness and expectation confirmation significantly predict users' satisfaction. Additionally, the ANN results highlighted that expectation confirmation was the strongest predictor of satisfaction. Furthermore, the sensitivity analysis results underscored that relatedness to technology was the most critical psychological need for predicting satisfaction. The findings revealed the critical role of basic psychological needs in predicting satisfaction with ChatGPT use. Confirmatory factor analysis supported the four-factor structure of the BPN-TU scale. In addition to these theoretical insights, practical recommendations are offered for service providers, decision-makers, and developers.