The effects of acute hypoxic exposure on mechanical output and internal responses during cycling with heart rate (HR) clamped at lactate thresholds 1 and 2 (LT1 and LT2, respectively) were investigated. On separate days, 12 trained males cycled for 15 min at a clamped HR corresponding to LT1 and LT2 under normoxic or hypoxic conditions (simulated altitude of ∼3500 m and inspired oxygen fraction of 13.6%). Power output (PO), arterial oxygen saturation, ventilatory and perceptual responses were measured every 3 min, with metabolic response assessed pre‐ and post‐exercise. At LT1, PO was consistently lower in hypoxia compared to normoxia (p < 0.01). At LT2, PO was not different between normoxia and hypoxia at 3 and 6 min (both p > 0.42) but was significantly lower in hypoxia at 9, 12 and 15 min (all p < 0.04). Overall, hypoxia induced a greater decrease in PO at LT1 (−33.3% ± 11.3%) than at LT2 (−18.0 ± 14.7%) compared to normoxia. Ventilatory, perceptual and metabolic responses were influenced by exercise intensity (all p < 0.01) but not environmental conditions (all p > 0.17). A simulated altitude of ∼3500 m is more effective in reducing cycling PO at LT1 than LT2 during HR clamped cycling while maintaining other internal loads. Therefore, normobaric hypoxia provides a greater benefit via a larger decrease in the mechanical constraints of exercise at lower exercise intensities.