A health crisis caused by a pandemic tested the effectiveness of national healthcare systems by testing both financing and organizational and technical performance of patient care. At that time, the structural flaws in healthcare systems and inequalities in the level of healthcare in its different dimensions and countries due to resource constraints were highlighted. Therefore, the paper concentrates on investigating how the crisis in the health system affects the quality of healthcare services as a result of changes in the availability of financial, material, and human resources belonging to this system. The quantitative data, in terms of healthcare characterizing the OECD countries and selected non-member economies, treated as an example of economically developed regions, were chosen for the analysis. The study included five areas of resources, i.e., demographic, financial, human, technical, and the delivery of basic services in healthcare. T-test method for dependent samples, supplemented with Hedge’s g statistics, was applied to test the differences between the mean values of individual indicators. The results indicate the occurrence of changes in some areas of the healthcare system due to a crisis. Identifying areas that are particularly vulnerable to sudden changes in the healthcare system helps to understand which resource areas need to be strategically managed first, as shifts in levels respond to deteriorating healthcare quality outcomes.