In high school, I experienced the same symptoms EVERY time I did intervals. I was fine during the workout, but when I stopped, I would feel as if I would black out ... would have to lie down immediately.
In my case, when I stopped a high-intensity workout, blood would pool in my legs, depriving my brain (I was told by an MD). Lying down would get the blood back to my brain. Continued jogging would keep the blood from pooling, also, but I tended to go all-out on that last 400, or whatever, and just stop.
Some people have a similar physiological response to the sight of blood and the like. Blood pools in their legs, and they pass out.