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The 2020 Zagreb earthquake occurred on Sunday 22 March 2020. This earthquake was the first that happened during the lockdown imposed by governments to stop spreading the COVID-19. This fact makes the event interesting as a multi-hazard phenomenon. The lockdown made it not possible to deploy an earthquake reconnaissance mission. Therefore, it was necessary to undertake a remote mission supported by the monitoring and analysing social media (SM) platforms, such as Twitter and Instagram. This paper presents details and analysis of this monitoring and how it may help understand the impacts of an earthquake. In our work, we first identified the hashtags related to the event. Through the LastQuake app, we obtained the intensity reports from affected people and comments and pictures useful for damage assessment. The team obtained 59,246 tweets posted between the 20th March and the 30th April 2020 and 31,911 comments from LastQuake app users written on the day of the earthquake. Images from posts and comments were used for remote assessment of damage in buildings. Sentiment analysis (SA) was applied to tweets and comments related to the event to assess emergency management during the relief phase after the earthquake. Our work shows that only a limited number of pictures collected through social media were suitable for damage assessment of individual buildings. However, they were still useful as a proxy estimation of damages in some areas of Zagreb and surroundings. We also found SA supported by machine learning a valuable method to assess and identify critical aspects of the emergency and early recovery post-disaster phases. Applying SA we identified the most affected areas, the damages in the non-structural elements in hospitals, the support of collaborative networks for the evacuation of patients and the role of Ministers in the early recovery.