Anelka, 31, was sent home from the World Cup after insulting France coach Raymond Domenech during the 2-0 defeat to Mexico and he was subsequently banned for 18 games after failing to attend a disciplinary hearing.
Anelka, who had indicated that he did not plan to play for his country again after South Africa, said in response to the FFF's ban: "These people are clowns. I'm dying with laughter."
The striker scored twice during Chelsea's Champions League victory on Wednesday, and he has now said his response to the goals was directed at the federation.
"It was just something for the French federation about what happened at the World Cup," he said. "It was just a little joke, but I think the other French players will understand what it means. What happened in the summer is in the past now and I'm 100% focused on playing for Chelsea."