"It's always difficult when a coach goes, and I had a very close relationship with Julian," Goretzka told ZDF broadcaster after Germany's 2-0 friendly international win over Peru.
"In the last year, I've probably seen him more than my family, so it is a shock," he added.
Kimmich said that he and his team-mates were at fault for the departure of Nagelsmann, who was sacked by Bayern on Friday.
"It's always disappointing when a coach is sacked, because it means we have not delivered as players," said Kimmich, who captained Germany in Mainz on Saturday.
He added that it had been strange to prepare for an international game amid the noise of Nagelsmann's dismissal.
"It's a curious situation, but that's the football business at the end of the day. There is not much heart, not much love."