The Belgium international suggested that Anelka's controversial 'quenelle' gesture was "not such a big deal" in an interview with Sky Sports News.
Anelka could face a five-game ban for making the alleged anti-semitic gesture against West Ham United in December after the Football Association charged the player on Tuesday.
"[Lukaku] wanted to just support a teammate, someone who he admires from a young age," BBC Sport quotes Martinez as saying. "He's still a young man.
"Sometimes at that age you can speak with your heart, and you don't realise that support to a human being people will see you supporting certain views. That's not the case. There's been a bit of a misunderstanding."
Anelka has until 6pm this evening to officially respond to the FA charge.