We study the acceleration of cosmic rays by collisionless structure formation shocks with ENZO grid simulations. Data from the FERMI satellite enable the use of galaxy clusters as a testbed for particle acceleration models. Based on advanced cosmological simulations that include different prescriptions for gas and cosmic rays physics, we use the predicted {\gamma}-ray emission to constrain the shock acceleration efficiency. We infer that the efficiency must be on average <0.1% for cosmic shocks, particularly for the 2Comment: 15 pages, 14 figures. MNRAS, accepted