Here is the percentage of oxygen in the air (as compared to sea level) at these altitudes:
8000 ft 76%
10000 ft 70%
12000 ft 65%
14000 ft 61%
As a consequence of the lower amount of oxygen in each breath:
1. the body with have to use more anaerobic power to maintain power levels
2. the heart rate will increase in an effort to supply more blood flow to the working muscles
Actually, the percentage of oxygen in air is 21% at sea level and at higher altitudes. What changes is the air density (and pressure) which drops by the amounts listed. So, it is certainly true that one takes in less oxygen (and nitrogen, etc. too) at higher elevations.