The effect of the featureless power-law (PL) continuum of an active galactic nucleus (AGN) on the estimation of physical properties of galaxies with optical population spectral synthesis (PSS) remains largely unknown. With this in mind, we fit synthetic galaxy spectra representing a wide range of galaxy star formation histories (SFHs) and including distinct PL contributions of the form $F_{ u} propto u^{-alpha}$ with the PSS code STARLIGHT to study to which extent various inferred quantities (e.g. stellar mass, mean age, and mean metallicity) match the input. The synthetic spectral energy distributions (SEDs) computed with our evolutionary spectral synthesis code include an AGN PL component with $0.5 leq alpha leq 2$ and a fractional contribution $0.2 leq x_{mathrm{AGN}} leq 0.8$ to the monochromatic flux at 4020 AA. At the empirical AGN detection threshold $x_{mathrm{AGN}}simeq 0.26$ that we previously inferred in a pilot study on this subject, our results show that the neglect of a PL component in spectral fitting can lead to an overestimation by $sim$2 dex in stellar mass and by up to $sim$1 and $sim$4 dex in the light- and mass-weighted mean stellar age, respectively, whereas the light- and mass-weighted mean stellar metallicity are underestimated by up to $sim$0.3 and $sim$0.6 dex, respectively. Other fitting set-ups including either a single PL or multiple PLs in the base reveal, on average, much lower unsystematic uncertainties of the order of those typically found when fitting purely stellar SEDs with stellar templates, however, reaching locally up to $sim$1, 3 and 0.4 dex in mass, age and metallicity, respectively. Our results underscore the importance of an accurate modelling of the AGN spectral contribution in PSS fits as a minimum requirement for the recovery of the physical and evolutionary properties of stellar populations in active galaxies.
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