Your experience is unfortunate, yet not terribly uncommon, saw it many many many times when i was a new-hire at Trans States, happened on a repeat basis until Feb-Mar 07, when some changes were made and extra sim sessions were awarded, before then, they'd just send you packing. Lots of those buddies are now off at other regionals, several at expressjet and are loving it there, so just remember that NO this isn't the end of the world.

As far as your question, technically, you did bust out of training. However, you most likely don't have a failure on your training record. You'll have to explain to individuals why you resigned from training, just be honest, explain what you learned from the situation, and move on. If the first company doesn't hire you, try again, eventually you'll find someone who will, and at some point in your career, this will just be a far distant memory.