Background: The aim of this study was to identify predictors of the unmet healthcare needs during the financial and recent health crisis in Greece. Methods: Time series analysis was performed for the years 2008 through 2022 using the Eurostat database. The dependent variable was the percentage of people who reported unmet need for medical care. Demographic, socioeconomic, and health data, as well as health expenditures, were used as independent variables. Correlation analysis and simple linear regression models were conducted to analyze the results. Results: Unmet health needs in Greece increased from the start of the crisis until 2016, as a gradual de-escalation of the crisis was observed. However, in 2019 the country recorded the second highest level of unmet needs for medical care before the health crisis. Limitations in usual activities, reporting bad/very bad health status, being unemployed, and having low income increased the likelihood of unmet needs. Health expenditures (public or private) were also significant determinants of unmet healthcare needs. Conclusions: The increased unmet health needs widen inequalities in health and healthcare access. Therefore, health policies should eliminate barriers which restrict the access to health and enhance healthcare services, developing conditions for citizens’ well-being.