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Threshold-voltage shifts and increases in 1/f noise are observed in proton-irradiated AlGaN/GaN high-electron-mobility transistors, indicating defect-mediated device degradation. Quantum mechanical calculations demonstrate that low-energy recoils caused by particle interactions with defect complexes are more likely to occur than atomic displacements in a defect-free region of the crystal. We identify the responsible defects and their precursors in the defect-mediated displacement mechanism. The electronic properties of these defects are consistent with the increases in threshold voltage and 1/f noise in proton irradiation experiments.