The African nation bowed out of the tournament in unceremonious fashion, with Song red-carded for elbowing Mario Mandzukic, while Assou-Ekotto appeared to headbutt teammate Benjamin Moukandjo in the dying minutes.
"It's unimaginable," Finke told reporters.
"I saw this happen and I need to find out exactly what happened, why exactly these two players exploded. I hate to see that. It's not the image of Cameroon I want to project."
Ivica Olic had fired the European outfit ahead, before the dismissal of the Barcelona midfielder altered the complexion of the clash.
Ivan Perisic doubled the advantage early in the second half, and a later brace from Mandzukic helped seal the win as Croatia kept alive hopes of reaching the last 16.