Song was sent off in the first half for elbowing Croatia striker Mario Mandzukic in the back, while Assou-Ekotto head-butted team-mate Benjamin Moukandjo in the 90th minute, as Cameroon's FIFA World Cup campaign fell apart.
Song and Assou-Ekotto's violent outbursts came on the back of rumours of unrest in the Cameroon camp with the players reportedly having threatened to boycott Brazil 2014 due to a pay dispute, while injured captain Samuel Eto'o was labelled a 'traitor' in the local press for a perceived disinterest in playing against Croatia.
With his team out of the running for a round of 16 berth, Finke apologised for their performance in Brazil and promised to investigate Song and Assou-Ekotto's behaviour.
"It's unimaginable," the German coach said after the game in Manaus.
"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."
"I apologise for the result, it really hurts," Finke said.
"We had no control on the game and I didn't like the behaviour of my team. We have to look forward - this team has players for the future."
"It's a tough result to take. It's always difficult to play with 10 men but that's still no excuse for tonight's performance," the 66-year-old said.
