Bayern players 'shocked' by Nagelsmann dismissal
"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."
Nagelsmann was sacked on Friday after a 2-1 defeat to Bayer Leverkusen saw Bayern slip behind title rivals Borussia Dortmund last weekend.
His successor Thomas Tuchel was presented in Munich on Saturday, with Bayern bosses expressing optimism that the former Chelsea and Paris Saint-Germain coach could turn a turbulent season around.
Kimmich, though, admitted that he had no relationship with Tuchel as of yet.
"I don't know him yet," he told ZDF.
Goretzka, meanwhile, seemed to question statements by Bayern sporting director Hasan Salihamidzic that there had been a split between Nagelsmann and the players.
"I'd be stupid to contradict my boss, but personally, I had no split with Julian," he said.
"We have to trust our bosses that they are making the right decision for the club," he added.