The Cameroon pair appeared to be arguing during stoppage time as Assou-Ekotto leaned in to headbutt Moukandjo, before Pierre Webo broke the altercation up.
"It's unimaginable. I saw this happen and I need to find out exactly what happened, why exactly these two players exploded," Finke told reporters.
"I hate to see that. It's not the image of Cameroon I want to project."
The loss meant that Cameroon have failed to progress further than the group stage in the previous five attempts.