When I was in college, I was reassured that it was normal when a superb, Olympic-caliber distance runner told me that she got winded walking up a lot of stairs, too.
Since then, I don't feel bad when I get tired from lots of stairs.
I do get angry at them though.
Case in point:
There is no reason that a company should ever leave the up escalator that is this long out of service like it was the other day when I was leaving a store in Manhattan. I don't know if you can get the full effect of their length just by looking at them, so if you need to count the stairs and then count the stairs on a normal staircase in your house or in your building, feel free. I estimated that this was about three, almost four, stories of straight stairs.
Walking up these stairs was so painful that I was out of breath and my legs were actually slightly burning for a while after finishing the climb.
On the bright side, I guess it was a good butt and thigh workout.