The Germany international, only starting due to Sami Khedira picking up an injury during the warm-up, clashed with Argentina's Ezequiel Garay during the first-half and received treatment on the pitch.
Kramer tried to continue but began to ask questions of Rizzoli which concerned the referee, leading him to recommend the midfielder's substitution.
He told Gazzetta dello Sport: "Shortly after he'd been struck by Garay, Kramer came to me, asking 'ref, is this the final?'
"I thought he was joking so I asked him to repeat the question, and he said: 'I need to know if this is really the final.'
"After I said 'yes', he was a bit stunned and said: 'Thanks, that's important to know.'
"I informed [Bastian] Schweinsteiger and they replaced Kramer."
Kramer is currently one season into a two-season loan at Borussia Monchengladbach from Bayer Leverkusen.
And Monchengladbach's director of sport felt it necessary to insist the player would complete the second season of his spell at the Bundesliga club following reported interest.
"Of course we would like to sign him permanently, but we're just happy to have him," Max Eberl told Germany's Sky Sport News. "Christoph Kramer will be spending this season with us. The fact that other clubs are realising how good he is doesn't concern us."
Meanwhile, Rizzoli has told of Nigeria goalkeeper Vincent Enyeama's fear of Lionel Messi when the sides met during the group stages of the tournament.
"[Enyeama] approached me with a smile on his face, and said: 'I told my teammates not to commit any fouls near the penalty area,'" Rizzoli explained.
"[Lionel] Messi puts them all away. He's phenomenal and he's going to make a real fool of me. They got my message.' When I think back to that, it still makes me smile."
Argentina went on to win the game 3-2 with Messi scoring twice, including a free-kick from outside the area.
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