The aim of this study is to identify and classify the most important factors affecting patient satisfaction in the COVID-19 pandemic crisis considering economic effects. This is an analytical study using the analytic hierarchy process (AHP) method and ANN-MLP (Artificial neural network based on multilayer perceptron model as a supervised learning algorithm) as an innovative methodology. The questionnaire was completed by 72 healthcare experts (N = 72). The inter-class correlation (ICC) coefficient value was confirmed in terms of consistency to determine sampling reliability. The findings show that interpersonal care and organizational characteristics have the greatest and least influence, respectively. Furthermore, the observations confirm that the highest and lowest effective sub-criteria, respectively, are patient safety climate and accessibility. Based on the study’s objective and general context, it can be claimed that private hospitals outperformed public hospitals in terms of patient satisfaction during the COVID-19 pandemic. Focusing on performance sensitivity analysis shows that, among the proposed criteria to achieve the study objective, the physical environment criterion had the highest difference in private and public hospitals, followed by the interpersonal care criterion. Furthermore, we used a multilayer perceptron algorithm to assess the accuracy of the model and distinguish private and public hospitals as a novelty approach. Overfitting results in finding an MLP model which is reliable, and the accuracy of the model is acceptable.