Aims. Radio observations have shown that galaxy clusters are giant reservoirs of cosmic rays (CR). Although a gamma-ray signal from the cluster volume is expected to arise through interactions of CR protons with the ambient plasma, a confirming observation is still missing. Methods. We searched for a cumulative gamma-ray emission in the direction of galaxy clusters by analysing a collection of stacked Fermi-LAT count maps. Additionally, we investigated possible systematic differences in the emission between cool-core and non-cool-core cluster populations. Results. Making use of a sample of 53 clusters selected from the HIFLUGCS catalog, we do not detect a significant signal from the stacked sample. The upper limit on the average flux per cluster derived for the total stacked sample is at the level of a few 10-11   ph   cm-2   s-1 at a 95% confidence level in the 1–300 GeV band, assuming power-law spectra with photon indices 2.0, 2.4, 2.8, and 3.2. Separate stacking of the cool-core and non-cool-core clusters in the sample lead to similar values of around 5 × 10-11   ph   cm-2   s-1 and 2 × 10-11   ph   cm-2   s-1, respectively. Conclusions. Under the assumption that decaying π0, produced in collisions between CRs and the ambient thermal gas, are responsible for gamma-ray emission, we set upper limits on the average CR content in galaxy clusters. For the entire cluster population, our upper limit on the gamma-ray flux translates into an upper limit on the average CR-to-thermal energy ratio of 4.6% for a photon index of 2.4, although it is possible for individual systems to exceed this limit. Our 95% upper limits are at the level expected from numerical simulations, which most likely suggests that the injection of CR at cosmological shocks is less efficient than previously assumed.