In this work we are using spatially localized acoustic resonances, so-called zero group velocity (ZGV) Lamb waves, to assess the attenuation parameters from the temporally decaying acoustic waves in thin plates. As these waves are not propagating, the temporal decay of these waves is directly linked to the intrinsic material damping. Guided waves and ZGV Lamb waves are excited and detected fully optically using frequency domain laser excitation and optical vibrometry. The measured responses are fitted with results obtained from finite element simulations. Samples of tungsten with thicknesses in the micrometer range, featuring ZGV frequencies around 2 GHz, were produced. As the damping of the ZGV resonance is influenced by both, the shear and longitudinal attenuation, two ZGV resonances are evaluated in order to assess the overall attenuation.