Motivated by the detection of a hardening in the γ-ray spectrum of the radio galaxy Centaurus A, we have analysed ∼10 years of Fermi-LAT observations of 26 radio galaxies to search for similar spectral features. We find that the majority of the radio galaxies' γ-ray spectral energy distributions are best fitted with a simple power-law model, and no spectral hardening similar to that found in Centaurus A was detected. We show that, had there been any such spectral features present in our sample of radio galaxies, they would have been seen, but note that 7 of the radio galaxies (3C 111, 3C 120, 3C 264, IC 4516, NGC 1218, NGC 2892 and PKS 0625-35) show evidence for flux variability on 6-month timescales, which makes the detection of any steady spectral features difficult. We find a strong positive correlation (r = 0.9) between the core radio power at 5 GHz and the γ-ray luminosity and, using a simple extrapolation to TeV energies, we expect around half of the radio galaxies studied will be detectable with the forthcoming Cherenkov Telescope Array.