He knew the exact moment when she died.
They had been standing together - he had been holding her, could feel the rising and falling of her breath - but that was only part of it.
From a certain standpoint, she was already dead twice over; no jinchūriki survived the extraction of their tailed beast, and no one survived being impaled by a claw so large it was longer than a human was tall.
That did not change the fact that he had been the one to directly end her life, when he sealed her chakra into Naruto with the Hakke Fuin.