Darth is correct.

Just like to say, if you think about it, you can stab someone, but they are still alive for a few seconds or minutes. So does that make it mean you killed them or they died after the fact due to blood loss etc etc?

I am thinking, even though Kakashi used his last remaning chakra to use Magenkyo Sharingan, I do believe enough damage was done to him by pain, to warrant Kakashi being killed by pain. He may not have died instantly, but he did die soon afterwards.

Just my thoughts on the matter.