Thanks to the Internet and mobile technologies, the collection of felt reports after global earthquakes is today remarkably efficient and rapid. Despite the volume of collected reports, it remains unclear whether felt reports on their own can provide a complete and rapid picture of earthquake’s effects, especially for damaging shaking levels. To answer this question, we analyze the response rates and time characteristics of 55,000 felt reports collected at the European‐Mediterranean Seismological Centre (EMSC) and 120,000 launches of its LastQuake smartphone application within an hour of the 108 global earthquakes studied. The number of reports corresponding to damaging shaking levels (intensity 7 and above) is very limited and, if any, they are collected much later than lower intensity level reports. Intensities 5–6 level reports are collected in significant numbers but typically 20 min after lower intensities. The application launches that benefit from having precise locations share similar variations in time and intensity levels as felt reports. First, we conclude that felt reports alone without their temporal characteristics are unlikely to rapidly provide a full and complete picture of damage related to global earthquakes. However, there is a general schematic pattern for data collected by EMSC named the doughnut effect in which damaged zones are free of felt reports and ultimately surrounded by intensities 5–6. This pattern is not a proof of damage but can be helpful to identify zones potentially affected by severe damage. For earthquakes with maximum intensities 5–6, the initial doughnut shape observed immediately after the earthquake rapidly disappears (about 20 min) as intensities 5 and 6 reports get shared by eyewitnesses.