The incident happened as Cameroon trailed by a goal and resulted in the Barcelona player receiving a straight red card near the end of the first half.
Although Song apologised for lashing out at the Bayern Munich forward, Mandzukic is insistent he went after him on purpose.
"The action was strange. Both of us were running and suddenly I felt a blow. I think that it was clearly on purpose," Mandzukic told German TV station, ZDF.
The 28-year-old – who scored two second-half goals in the win – recently revealed that he would be departing his club side Bayern as a result of not being able to adapt to Pep Guardiola’s tactics last season.
Despite being linked to a host of clubs since confirming his departure from the German champions, Mandzukic has now refused to speak about his future and says he is only focusing on doing well with Croatia in Brazil.
“Now is not the time to think about those things. I'm focused on the World Cup and my team,” he said.
Mandzukic will next be in action when Croatia take on Mexico on June 23 in Recife.