Centaurus A (Cen A) is the nearest radio galaxy discovered as a very-high-energy (VHE; 100 GeV–100 TeV) γ-ray source by the High Energy Stereoscopic System (H.E.S.S.). It is a faint VHE γ-ray emitter, though its VHE flux exceeds both the extrapolation from early Fermi-LAT observations as well as expectations from a (misaligned) single-zone synchrotron-self Compton (SSC) description. The latter satisfactorily reproduces the emission from Cen A at lower energies up to a few GeV. New observations with H.E.S.S., comparable in exposure time to those previously reported, were performed and eight years of Fermi-LAT data were accumulated to clarify the spectral characteristics of the γ-ray emission from the core of Cen A. The results allow us for t...