A goal from Mergim Berisha just before the hour at Augsburg Arena condemned Bayern to its first defeat of the season.
It also made it four games in the Bundesliga without a win for the defending champion, its longest period without tasting victory in the league since the 2001-2002 season.
Speaking at a press conference alongside Augsburg boss Enrico Maassen after the game, Nagelsmann praised the victors, but believed his team should still have won the game.
"Congratulations to Augsburg and Enrico for their victory against us," he said. "If I look at the statistics I think we should win that game, if we properly defend that free-kick [that led to the goal].
"It was difficult to break them down after it went to 1-0."
Bayern had 19 shots to the hosts' 11, However, according to Opta, Augsburg shaded it in terms of expected goals, by 1.56 to 1.52.
Few visiting players shone, and it was another struggle for Sadio Mane, who only had one shot at goal, fewer even than Bayern goalkeeper Manuel Neuer (two) who came up for late set-pieces.
"I won't be talking about individual players here, I will speak to them directly," Nagelsmann said. "There's always a difference between what I tell you and what I tell the team."
Augsburg ended Bayern's record streak of 87 Bundesliga games with at least one goal, having done similar in 2014 when ending their Bavarian neighbour's previous record streak of 65 games with a goal.
That, naturally, led to questions about former striker Robert Lewandowski, who scored twice for Barcelona in its 3-0 win over Elche in LaLiga at the same time Bayern was losing at Augsburg.
On the question of missing a number nine, Nagelsmann quipped: "What will you do if I say 'yes' or if I say 'no'? We have the classic nine with [Eric Maxim] Choupo [Moting] and we subbed him in today.
"It doesn't matter what I say now. If I say 'no' you’ll say I don't see the problem, if I say 'yes' you’ll say we're missing Lewandowski."
At the end of the press conference, Nagelsmann added: "I'm thinking about all things. About the situation, about myself, about everything."
His opposite number was grateful for the kind words, and Maassen explained his team had won by taking risks.
Although Bayern had 10 shots to the host's two in the second half, Augsburg matched its efforts in the first 45 minutes when both recorded nine shots each.
"Thanks to Julian [for his congratulations]," Maassen said. "I'm very pleased with how my team played.
"We were willing to take risks, I told the team we could defend and maybe lose 1-0 or 2-0, or we could play high-risk. We could concede more goals, but we'd also have a chance to win, and you have to attack if you want to try and beat them, so we ran after plenty of balls.
"We gave away a lot of chances, but [goalkeeper Rafal] Gikiewicz was tremendous."