The seismic events that struck central Italy in 2016 caused severe damage to a wide range of buildings and infrastructures. Masonry buildings were particularly affected even for low values of peak ground acceleration. In this paper, the data recorded by three masonry buildings belonging to the Seismic Observatory of Structures (OSS) network are used to detect their seismic damage by means of Spectral Entropy (SE). However, entropy measures are sensitive to the energy inserted in the system, since an input of energy can bring to a more deterministic behavior of the structure and thus to a reduction of the entropy indicator. When non-stationary time series are used to evaluate the presence of damage (e.g. mild seismicity) the entropy of the system could be underestimated, leading to misleading results. For these reasons, in this paper an indicator based on the SE is proposed to assess the occurrence of damage also in presence of mild seismicity.