The control of non-radiative losses in light-emitting diodes (LEDs) based on metal halide perovskites is crucial to improve device efficiency. Recent studies have shown a correlation between lattice strain and electron-hole recombination. To consolidate the concept, we investigate how external pressure (strain) affects the crystal structure, electronic properties, point defect concentration, and luminescence efficiency of CH3NH3PbBr3. Relativistic first-principles calculations reveal enhanced Rashba splitting and Schottky defect disorder under compression, which produce a pronounced decrease in the electroluminescence peak energy and intensity in operating CH3NH3PbBr3 LEDs. The resulting model sheds light on the factors underpinning the intricate strain-property relationships in soft crystalline semiconductors.