Nagelsmann, a Bundesliga winner in charge of Bayern Munich in 2022, took over the national team in 2023, but they only reached the quarter-finals of the 2024 Euros they hosted.
Their World Cup campaign in North America started well, thrashing newcomers Curacao 7-1 and then coming from behind to defeat Ivory Coast 2-1.
They lost 2-1 to Ecuador in their final group game - although they had already guaranteed top spot - but the manner of this loss to Paraguay leaves Nagelsmann fighting for his job, with plenty of calls already on social media for ex-Liverpool manager Jurgen Klopp to replace him.
"If you consider the whole tournament, the way we played, it is a deserved loss," former Germany defender Arne Friedrich said on BBC Radio 5 Live.
"Nagelsmann has to face the consequences. It is very disappointing, but that is sport. I would definitely say the journey continues without Nagelsmann."
Former Germany midfielder Thomas Hitzlsperger, speaking on BBC One, added: "It's hard to explain how Germany got into this tournament with so many problems. It's unacceptable.
"It doesn't look good for Nagelsmann. In the last few months, he hasn't dealt with situations well. With the expanded World Cup format, to go out so early would be tough to take for any big nation."
Immediately after the game, Nagelsmann was repeatedly asked about his future and said he was "not someone who runs away" but admitted he would not be popular among the German supporters.
"If we're going to do a survey today in Germany, people are not going to speak about me positively obviously," he added. "I did feel the support in the stadium. I don't think everyone in Germany will agree with me staying on and continuing as manager of the team.
"I'd like to praise all the German fans who came to the stadium. I expected a totally different reaction from them but it was amazing and impressive the way they supported us, even after the defeat.
"I'm not going to step back only because we are eliminated. If the DFB [German football association] want me to continue, I am going to continue. I know how the industry works and a lot of people now want me to leave. I want to continue if the German FA wants me to."
Even before the Paraguay game, Nagelsmann was getting criticism, with Klopp - working for German television - unhappy with the performance against Ecuador, saying: "We chose the wrong methods on this pitch; we played the wrong kind of football against an aggressive opponent."
But those lessons were not learned against a physical, dogged and determined Paraguay side that defended deep and in numbers and frustrated Germany.
Paraguay now play either France or Sweden in the last 16 on Saturday, while Germany have to deal with another early exit.
"If I want to be cynical and sarcastic, all we would have earned is a right to get absolutely destroyed by France," said German football journalist Raphael Honigstein on BBC Radio 5 Live.
"You can get knocked out, but you can't get knocked out against Paraguay at this stage in this manner. That is why this is not going to be a defeat without repercussions and an aftermath.
"If you look at the whole tournament, it just wasn't enough. Germany has been poor.
"There were too many big calls not coming off for Julian Nagelsmann. It is going to be very hard for him to survive this. I think it will be over for him, I am afraid."
