[dhimes]

If you get the chance to try it again, don't just stop suddenly when you have finished the exercise, but do a small warm-down phase of very little effort. That may keep the pass-out response at bay.

I'm not sure if this is a vasovagal response or not (http://en.wikipedia.org/wiki/Vasovagal_response) but I have this response also. In fact, mentioning it to my doc won me a full cardio work-up from a cardiologist. I get the response from intense weight-lifting and anaerobic cardio exercise (like what you describe) if I suddenly stop. If, however, I keep doing very light exercise, I don't "nearly" pass out (I've never fully passed out from it, only gotten to the dim-vision gray-out/dizziness described here, so I think I was close to passing out but not exactly sure).