The patient safety climate is a key element of quality in healthcare. It should be a priority in the healthcare systems of all countries in the world. The goal of patient safety programs is to prevent errors and reduce the potential harm to patients when using healthcare services. A safety climate is also necessary to ensure a safe working environment for healthcare professionals. The attitudes of healthcare workers toward patient safety in various aspects of work, organization and functioning of the ward are important elements of the organization’s safety culture. The aim of this study was to determine the perception of the patient safety climate by healthcare workers during the COVID-19 pandemic. Methods: The study was conducted in five European countries. The Safety Attitude Questionnaire (SAQ) short version was used for the study. A total of 1061 healthcare workers: physicians, nurses and paramedics, participated in this study. Results: All groups received the highest mean results on the stress recognition subscale (SR): nurses 98.77, paramedics 96.39 and physician 98.28. Nurses and physicians evaluated work conditions (WC) to be the lowest (47.19 and 44.99), while paramedics evaluated perceptions of management (PM) as the worst (46.44). Paramedics achieved statistically significantly lower scores compared to nurses and physicians in job satisfaction (JS), stress recognition (SR) and perception of management (PM) (p < 0.0001). Paramedics compared to nurses and physicians rank better in working conditions (WC) in relation to patient safety (16.21%). Most often, persons of lower seniority scored higher in all subscales (p = 0.001). In Poland, Spain, France, Turkey, and Greece, healthcare workers scored highest in stress recognition (SR). In Poland, Spain, France, and Turkey, they assessed working conditions (WC) as the worst, while in Greece, the perception of management (PM) had the lowest result. Conclusion: Participant perceptions about the patient safety climate were not at a particularly satisfactory level, and there is still a need for the development of patient safety culture in healthcare in Europe. Overall, positive working conditions, good management and effective teamwork can contribute to improving employees’ attitudes toward patient safety. This study was carried out during the COVID-19 pandemic and should be repeated after its completion, and comparative studies will allow for a more precise determination of the safety climate in the assessment of employees.