Anelka exploded in a foul-mouthed tirade after the coach criticised him for straying out of position during the goalless first half of their 2-0 Group A defeat by Mexico on Thursday.
The 31-year-old was subsequently substituted before the start of the second half.
Domenech stressed earlier today that had Anelka apologised he would have allowed him to stay with the squad.
He also played down the seriousness and context of his disagreement with the Chelsea striker.
"It was not a confrontation," said the 57-year-old, whose six-year reign as France boss will end with the country's participation in the South Africa as he is being replaced by 1998 World Cup-winner Laurent Blanc.
"People cannot imagine the pressure. We are in a dressing room, the coach says something to a player who is already under pressure, he can react angrily, and with strong words.
"He did not react in the most suitable fashion, but it was just a guy sitting in his corner and muttering - that would not have mattered had it stayed there. What was important was that it made the front page of a newspaper, and that exposes the internal life of the squad.
"I sorted out the problem internally, and as far as I was concerned it was done and dusted. I had another chat with him (Anelka) the next day and I left open the possibility for him to apologise, something which he did not want to do.
"The decision to exclude him was the right one. He does not have the right to say such things."