Background: The aim of this study was to assess the quality of assistance provided by emergency medical service (EMS) and hospital emergency department (ED) staff in the opinion of patients. Methods: Simple random sampling was performed to select the responders. A group of 131 people who correctly completed the questionnaire form was included in the study. The questionnaire was directed only to patients receiving EMS and/or ED assistance during the time period when the pandemic was announced in Poland. Results: Problems in the ED were reported by 38 people (31.15%), and calling EMS was reported as generating problems by 7 people (16.67%). Dissatisfaction with the help provided in EDs was reported by 33 patients (27.05%), and dissatisfaction with the help by EMS was reported by eight people (19.05%). The assessment of the patient’s satisfaction level significantly correlated with the waiting time in the ED (Spearman = 0.217; p = 0.016) as well as with the waiting for EMSs (Spearman = 0.403; p = 0.008). Conclusions: Patients of the ambulance service and hospital emergency departments during the pandemic positively assessed the actions of medical services, despite significant delays in providing health services.