Context. About 40% of the observation time of the High Energy Stereoscopic System (H.E.S.S.) is dedicated to studying active galactic nuclei (AGN), with the aim of increasing the sample of known extragalactic very-high-energy (VHE, E > 100 GeV) sources and constraining the physical processes at play in potential emitters.Aims. H.E.S.S. observations of AGN, spanning a period from April 2004 to December 2011, are investigated to constrain their gamma-ray fluxes. Only the 47 sources without significant excess detected at the position of the targets are presented.Methods. Upper limits on VHE fluxes of the targets were computed and a search for variability was performed on the nightly time scale.Results. For 41 objects, the flux upper limits we derived are the most constraining reported to date. These constraints at VHE are compared with the flux level expected from extrapolations of Fermi-LAT measurements in the two-year catalog of AGN. The H.E.S.S. upper limits are at least a factor of two lower than the extrapolated Fermi-LAT fluxes for 11 objects Taking into account the attenuation by the extragalactic background light reduces the tension for all but two of them, suggesting intrinsic curvature in the high-energy spectra of these two AGN.Conclusions. Compilation efforts led by current VHE instruments are of critical importance for target-selection strategies before the advent of the Cherenkov Telescope Array (CTA).