Kalinic, 30, who was starting his fourth successive worldwide on the bench, claimed he had a back injury before telling Dalic he was unable to play.
"He warmed up for the game against Nigeria, he was supposed to go in, but he said he was not ready".
"However, he said he wasn't ready to go on because he felt a back problem".
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Kalinic, who was unable to break into the starting lineup during the build-up to the tournament, also missed a warm-up friendly with Brazil and did not train on Sunday.
"I accepted it calmly, because I need ready and healthy players who can help their teammates".
However, in a short statement before training at Croatia's base in Roshchino, north-west of Saint Petersburg, Dalic claimed injury was the reason for Kalinic's return to Croatia.
Croatia faces Argentina this Thursday and according to Federation Internationale de Football Association rules, no replacement for Kalinic will be allowed meaning Dalic will have 22 players at his disposal under the end of the tournament.
After making a positive start to their World Cup campaign, Kalinic's departure will no doubt impact Croatia's preparations, as the 30-year-old was one of only two out-and-out strikers, alongside the man he was suppose to replace - Mandzukic.