Well when you reach your maximum level, maintain that level. If at first you don't succeed (most don't) keep trying. You train yourself (muscles and mental intensity) to push that hard. It really is a trained level. Being able to work throught that heart rate and the sheering pain of the lactic build up is a trained behaviour and can come with time.

Some say with sports in general you have to be a mascocist of sorts. Learn to enjoy and thrive harder with the intensity.

As for perceived. When I used to workout regularily, for example, I would load the weight to my max. I would reach a perceived failure. This is when my brain is screaming to stop because the intesity is tooo tough for my body. In reality I could usually pull out 1 or 2 more. When I trained people this difference (between brain failure and actual physical failure) was greater sometimes 4 to 5 reps depending on the persons individual intensity. While you dn't always want to train in this range of intensity it is important.