The Europeans booked their spot in the semi-finals after routing Brazil in Madrid on Wednesday.
Serbia exacted revenge against Brazil, having lost to them by 12 points in the group stage, leading at every break on their way to victory and a final-four showdown with France.
"Well it's a great game for us, great win," Kalinic told reporters.
"We played very well in the first half as in the second but at the start of the second we played even better, we played physical.
"In our first game here in the championship we didn't manage to play as physical as Brazil play and I think that was the key from the start of the game.
"We started to play tough, to play hard D [defence], to run and at the end that gave a result."
Coach Sasha Djordjevic said Serbia's concentration throughout was key to stopping a Brazil team usually dominant in transition.
"Our players had a great night, focused, hard, physical, smart, very smart.
"This really was a good game for us, important game for all, basketball where we are coming from because it's something else.
"This was really something I have to thank to my players with all my heart because they really did a great job.
"As Nikola [Kalinic] said, we played physical, we managed to stay focused every minute on the floor. And in each quarter they [Brazil] scored less than 20 points. "