The Bavarians were eliminated at the quarter-final round after losing 2-1 on aggregate to Spanish outfit Villarreal this week.
Bayern only have the Bundesliga title left to play for and Nagelsmann reveals the online abuse has increased after the Villarreal encounter.
"I can handle criticism well. The situation is different with the 450 death threats on Instagram," the German tactician told reporters, as per Goal.
"I actually get that after every game, whether we win or lose. I don't actually read them. I always delete a lot. Usually I only see the first line there.
"It's clear that a lot of people want to kill me, but now they're also shooting at my own mother, who has nothing to do with football and the elimination. That's a bit wild thenm but if I look at all of this, then I won't be able to finish.
"How do I deal with it? I don't give a sh*t. People should write what they want, but think a little more about it. I can not understand."