To understand the public sentiment toward the measures used by policymakers for COVID-19 containment, a survey among representative samples of the population in seven European countries was carried out in the first two weeks of April 2020. The study addressed people's support for containment policies, worries about COVID-19 consequences, and trust in sources of information. Citizens were overall satisfied with their government's response to the pandemic; however, the extent of approval differed across countries and policy measures. A north-south divide in public opinion was noticeable across the European states. It was particularly pronounced for intrusive policy measures, such as mobile data use for movement tracking, economic concerns, and trust in the information from the national government. Considerable differences in people's attitudes were noticed within countries, especially across individual regions and age groups. The findings suggest that the epidemic acts as a stressor, causing health and economic anxieties even in households that were not directly affected by the virus. At the same time, the burden of stress was unequally distributed across regions and age groups. Based on the data collected, we draw lessons from the containment stage and identify several insights that can facilitate the design of lockdown exit strategies and future containment policies so that a high level of compliance can be expected.