The 26-year-old was dismissed 40 minutes into the match after an off-the-ball incident with Mario Mandzukic.
Song told reporters: "I feel I have let my country and myself down.
"It was a stupid moment and I'm truly sorry. If I could do anything to take it back I would. Please forgive me."
Cameroon will now face Brazil on Monday, knowing that it will be their final match of the 2014 World Cup.