Energetic feedback from active galactic nuclei (AGNs) is often used in simulations to resolve several outstanding issues in galaxy formation, but its impact is still not fully understood. Here we derive new constraints on AGN feedback by comparing observations and simulations of the thermal Sunyaev-Zeldovich (tSZ) effect. We draw on observational results presented in Spacek et al. (2016, 2017) who used data from the South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT) to measure the tSZ signal from >= 10^11 M_Sun and >= 1 Gyr galaxies at z=0.5-1.0 (low-z) and z=1.0-1.5 (high-z). Using the large-scale cosmological hydrodynamical simulations Horizon-AGN and Horizon-NoAGN, which include and omit AGN feedback, we extract simulated tSZ measurements around galaxies equivalent to the observational work. We find that the Horizon-AGN results only differ from the SPT measurements at levels of 0.4 sigma (low-z) and 0.6 sigma (high-z), but differ from the ACT measurements by 3.4 sigma (low-z) and 2.3 sigma (high-z). The Horizon-NoAGN results provide a slightly better fit to the SPT measurements by differing by 0.2 sigma (low-z) and 0.4 sigma (high-z), but a significantly better match to the ACT measurements by differing by only 0.5 sigma (low-z) and 1.4 sigma (high-z). We conclude that, while the lower-mass (<~ 5 x 10^11 M_Sun) SPT results allow for the presence AGN feedback energy, the higher-mass (>~ 5 x 10^11 M_Sun) ACT results show significantly less energy than predicted in the simulation including AGN feedback, while more closely matching the simulation without AGN feedback, indicating that AGN feedback may be milder than often predicted in simulations.