The 26-year-old has also insisted that he will not travel to Euro 2016 unless he is guaranteed a starting spot in the team following the dispute, which saw Cacic accuse Lovren of not warming up for a friendly against Hungary.
Cacic said at the time: "I will not tolerate such behaviour because no-one is more important than the team. Lovren made a step backward, away from our squad. We didn't talk after the match, we will see what is going to happen, but I will not tolerate such acts and he made a wrong move."
Speaking to Croatian newspaper Sportske Novosti, a defiant Lovren refused to back down as he gave his version of the incident in Budapest.
"I will not apologise, I will either travel to France as a starting player or I am not going," he said. "I always get angry when the media comes out with half-truths so, to tell you what happened, the conditioning coach came to me and told me to go and warm up for 10 to 15 minutes. I said okay and I started to warm up. After 15 minutes, when I finished warming up, I began to get cold because I didn't have a jacket so went back to the bench.
"Then, after a minute, the fitness coach comes again and asks me, 'So why did you sit on the bench?' I told him he said to warm up for 10 to 15 minutes and I did it. Then he immediately said that to Cacic. Look, nobody in the world does not work [after] such long warming up. At Liverpool, when warmed up, we enter the game or after 15 minutes go back to the bench.
"I was told I would play the second half in Budapest. I was ready and also, the coach said we will all get a chance. And I didn't."
Croatia have been drawn against Spain, Turkey and Czech Republic in Group D at the tournament in France.