Kalinic, who played for Blackburn Rovers between 2009 and 2011, was starting his fourth global in a row on the bench and complained of the same problem in the friendly loss to Brazil.
But asked to come on in the 85th minute, it's claimed Kalinic complained of a back problem and refused to enter the fray - something which didn't convince his manager.
"Kalinic warmed up against Nigeria, but when he came out he told me that he wasn't ready".
Dalic did not answer any further questions or go into the matter any further.More news: At least 5 die when SUV crashes during chase
"However, he said he wasn't ready to go on because he felt a back problem. The same thing happened against Brazil and in training on Monday".
It seems the decision was later taken to axe the AC Milan forward with Kalinic believed to be taking the first flight back home from Russian Federation this week.
The 30-year-old's absence means Croatia lack a specialist alternative to Mario Mandzukic, although Andrej Kramaric - who started the Nigeria game playing off the Juventus man - can lead the line if needed.
"I accepted it calmly, because I need ready and healthy players who can help their teammates".
Croatia face Argentina in Nizhny Novgorod on Thursday, and it looks as though Dalic will prepare for the fixture with the disadvantage of being able to call upon only 22 players.