The German giants were eliminated from Europe's premier club competition after falling to a 2-1 aggregate defeat against Villarreal.
Bayern were clear favourites to progress against the Spanish side, however an Unai Emery masterclass set up the La Liga side to face Liverpool in the semi-finals for a spot in the showpiece event at the Stade de France in Paris.
Nagelsmann has largely enjoyed a decent first season in charge of Bayern, with the club sitting nine points clear at the the top of the Bundesliga, however they did suffer a shock second round defeat in the German Cup after losing 5-0 to Monchengladbach.
Criticism from fans is all part and parcel of life as a football manager, but according to Nagelsmann, things have now gone too far.
Speaking to the press, he said: "I know I will always get criticism from all sides - that's normal and I can deal with it.
"But with 450 death threats on Instagram, it's not so easy."
"If people want to kill me that's one thing, but they also attack my own mother, who doesn't even care about football," added Nagelsmann.
"I don't understand it. As soon as they turn off the TV, people forget all decency. And they think they are the ones in the right, that's the crazy thing."
Asked if he's considered legal action, he said: "I would never be done with it. I get them after every single game, regardless of whether we win or lose.
"There are more death threats when we play with a back three than when we play with a back four, and obviously a few more whenever we lose."