The Queens Park Rangers defender headbutted Moukandjo during the Indomitable Lions' 4-0 defeat against Croatia earlier this week.
"It all started with the first match against Mexico," Assou-Ekotto is quoted as saying by ESPN. "Moukandjo was on my flank, he tried to dribble past two opponents and lost the ball. I told him he should pass it to me. He replied I was right.
"The same situation happened against Croatia again. Everyone can make a mistake. But when I told him again, he replied: 'Get off my back!'. I could not accept his reaction. There was so much frustration in that match. Now people take me for an idiot.
"I could not control my temper. If the score was 0-0, it would have not happened. When we went back to the changing-room, Samuel Eto'o talked to me, but I was so angry that I didn't admit I was wrong. The next day, we met with Moukandjo again during breakfast and we shook hands."
Cameroon take on Brazil in their final World Cup Group A game.