Goals from Thomas Muller, Joshua Kimmich and a second-half Sebastian Griesbeck own goal set up the win for the Bavarians, before the hosts grabbed a late consolation from Cedric Itten.
“In the end, it’s important to have won against a newly-promoted side and to have done so in a game where we finished with 10 men,” Nagelsmann said.
“We started well. After the goal, Furth lost their sense of respect for us and played very well.
“We’re happy about the three points, Furth asked a lot of us.
“We would have liked to have kept a clean sheet, but we stayed ahead throughout. So, all’s well.”
Bayern were reduced to 10 men in the 48th minute when Pavard committed a tackle adjusted to be a last man foul.
“I think the tackle wasn’t absolutely necessary now,” Nagelsmann said.
“But I think we can still defend it like that. I hope it’ll only be two games (suspension).
“I also think that this is a red card. It affects the Achilles tendon, which is usually not a good area to slide.”