Having lost their opening Group A fixture 1-0 to Mexico, Cameroon slumped to a 4-0 defeat against Niko Kovac's side.
Aside from the sorry loss, Cameroon were further hindered by Alex Song's red card for needlessly elbowing Mario Mandzukic in the back, while Benoit Assou-Ekotto headbutted his own team-mate Benjamin Moukandjo following an angry exchange.
The Cameroon football authorities have taken a dim view of the flashpoints and are now carrying out an inquiry.
"The recent acts of violence that took place during the match against Croatia do not reflect the values of fair play and respect as promoted by our federation, staff and national team as a group," read a statement on the federation's website.
"As expressed by our coach during his press conference after the match, it is important that our team remains focused for its last game against Brazil.
"The mentioned disgraceful behaviour is being further investigated internally, and will be up for sanction if so judged by the mandated internal bodies."
Cameroon can no longer reach the knockout stages and face their last group match with hosts Brazil on Monday.
