“That was the correct decision,” Nagelsmann said.
“Matthijs played a good game. It’s a pity he conceded the penalty, but it happens. We move on.”
The result leaves Bayern in top spot for now, but SC Freiburg and Union Berlin can go past them with victories in Sunday’s games.
Nagelsmann admitted his side started slow after their midweek 2-0 UEFA Champions League win over Inter Milan.
“We weren’t great in the first 30 minutes, that’s often the case after a Champions League game,” he said.
“Then we played very well for 15 minutes and deserved to be ahead. The first 15 minutes of the second half were also decent enough.
“We had enough chances to score a third. In the end, Stuttgart took a lot of risks, we had good chances on the counter, but lacked that bit of quality.
“It was one of those classic scenarios where you leave your opponent thinking there’s still something left in the game for them, and they grab a draw with a penalty in stoppage time.
“We’ll train tomorrow, train on Monday, prepare and try to come up with a good plan ahead of the Barcelona game.”
Rivals Borussia Dortmund spurned the chance to go top after a 3-0 loss to RB Leipzig in Marco Rose’s first game in charge.