X-ray absorption spectroscopy (XAS) yields direct access to the electronic and geometric structure of hybrid inorganic-organic interfaces formed upon adsorption of complex molecules at metal surfaces. The unambiguous interpretation of corresponding spectra is challenged by the intrinsic geometric flexibility of the adsorbates and the chemical interactions with the interface. Density-functional theory (DFT) calculations of the extended adsorbate-substrate system are an established tool to guide peak assignment in X-ray photoelectron spectroscopy of complex interfaces. We extend this to the simulation and interpretation of XAS data in the context of functional organic molecules on metal surfaces using dispersion-corrected DFT calculations within the transition potential approach. For the prototypical case of 2H-porphine adsorbed on Ag(111) and Cu(111) substrates, we follow the two main effects of the molecule/surface interaction onto the X-ray absorption signatures: (1) the substrate-induced chemical shift of the 1s core levels that dominates in physisorbed systems and (2) the hybridization-induced broadening and loss of distinct resonances that dominate in more chemisorbed systems. Published by AIP Publishing.