Thermoacoustic instabilities in gas turbines and aeroengine combustors fall within the category of complex systems. They can be described phenomenologically using nonlinear stochastic differential equations, which constitute the grounds for output-only model-based system identification. It has been shown recently that one can extract the governing parameters of the instabilities, namely the linear growth rate and the nonlinear component of the thermoacoustic feedback, using dynamic pressure time series only. This is highly relevant for practical systems, which cannot be actively controlled due to a lack of cost-effective actuators. The thermoacoustic stability is given by the linear growth rate, which results from the combination of the acoustic damping and the coherent feedback from the flame. In this paper, it is shown that it is possible to quantify the acoustic damping of the system, and thus to separate its contribution to the linear growth rate from the one of the flame. This is achieved by postprocessing in a simple way simultaneously acquired chemiluminescence and acoustic pressure data. It provides an additional approach to further unravel from observed time series the key mechanisms governing the system dynamics. This straightforward method is illustrated here using experimental data from a combustion chamber operated at several linearly stable and unstable operating conditions.