Originally Posted by WillR

Depends what you mean by 'levels'. The fractional concentration of oxygen remains 20.93%. The partial pressure of oxygen falls in proportion to the ambient cabin pressure.

At 2100m of cabin pressurisation, the barometric pressure falls to 586mmHg, reducing oxygen pressure from 159.6mmHg to 122.6mmHg. Following humidification in the nose, the pressure of oxygen in the lung then becomes around 60mmHg (complicated formula; google the 'alveolar gas equation' if you're interested in more details).

This is low enough to cause significant hypoxia and shortness of breath in people with even mild to moderate lung disease.
So yes, it could cause your shortness of breath.

The other possibilities for an urge to breathe can include atelectasis (collapsed alveoli needing a deep breath to reinflate them), stimulation of certain stretch receptors, and a myriad of other things.