Anelka was kicked out of the French squad on Saturday after insulting Domenech at halftime in their 2-0 defeat by Mexico in their Group A game in Polokwane on Thursday.
The player's crude remarks were printed on the front page of French sports daily L'Equipe on Saturday and later that day the French Football Federation decided to send Anelka home.
"The only thing I reproach him (for) is that I gave him a chance to speak about it the next day and he refused," Domenech told French television channel TF1.
"People don't imagine the pressure we have," the coach said when asked why Anelka had insulted him. "When the coach makes remarks, a player can lose his nerve and have words."
Domenech, who decided after hearing the insults to take Anelka off for the second half, said the problem could have been resolved internally if the insults had not been published.
"It became important because it was in the newspaper," he said. "I had solved the problem because I had taken him off."
French media suggested on Sunday that Anelka's attitude was not the only problem in France's troubled squad and reported rival playmakers Yoann Gourcuff and Franck Ribery had a fight on the flight back from Polokwane.
"That's absolute nonsense," Domenech said when asked about that report. "Those who know Yoann a bit know it is totally impossible for him to fight with anybody."
France's fate is now out of their hands and even a big win over South Africa in their final group game in Bloemfontein on Tuesday might not be enough for them to survive the group stage.
"There's a tiny chance," said Domenech, aware that a draw between Mexico and Uruguay would put both France and the hosts out of the tournament. "We must win, score goals and hope things go our way."
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