Live by the blade, die by the blade.
Kakashi had heard that somewhere. He wasn't sure where, but it seemed to fit the life of a shinobi perfectly. At the same time, he thought, it was a horrible contradiction. To the civilians of the village, the shinobi were honorable tools, but when analyzed, they were far from it. In Academy they try to wean you from such thoughts, and eventually you learn.
As a tool, it is your job to do your job, and not get killed until you were needed. That was why, when you were confronted with an enemy stronger than you, you slit his throat from behind, in the dark without remorse. That was why ANBU were so secretive. They would not speak of thier dishonor. That was why kunoichi always broke at some point or another; sent on missions so degrading, looking for information. That was why no kunoichi was ever innocent.
So, for Kakashi to die by the treachery of a civilian made perfect sense. He could feel the poison running through his viens, injected by a civilian he hardly knew. He lived by the blade, and would now die without the blade, the perfect dishonor.
The perfect dishonor for a dishonorable shinobi.