Breathlessness isn't caused by lack of oxygen.
The urge to breathe comes mainly from carbon dioxide: chemoreceptors in your brainstem sense how CO2 lowers the pH of your spinal fluid and trigger the breathing drive as levels rise. Oxygen only matters once it has dropped a long way. That is why holding your breath feels unpleasant well before oxygen actually runs short.
Useful: It explains why hyperventilating before a dive is dangerous: it mutes the warning signal, not the oxygen use.
Source: en.wikipedia.org