The West Brom forward is facing the possibility of a five-match ban for making the gesture after scoring in December's 3-3 draw with West Ham, with the salute said to carry racist and anti-Semitic connotations.
Anelka defended the salute by claiming it was anti-establishment not anti-Semitic and said he was paying tribute to comedian friend Dieudonne M'bala M'Bala.
Lukaku - who is on loan at Goodison Park from Chelsea - was reported to have told Sky Sports: "I don't think he should be banned, he was just supporting a comedian in France. We don't have to make such a big deal about it."
The 20-year-old has since sought to clarify his stance, and insists he was merely showing support for former Stamford Bridge team-mate Anelka and not endorsing the use of the gesture.
In a statement released by anti-racism group Kick It Out - for whom Lukaku is an ambassador - he said: "I want to make clear that I was supporting a friend and player I have admired since I was a child.
"I apologise if I caused any offence with my comments as this was never my intention. There has been a misunderstanding and I want to clarify that I was in no way endorsing the gesture made by Nicolas.
"I am proud to be a ‘Next 20’ ambassador for Kick It Out and will continue to inform young people of the harmful effects discrimination of any kind can have."
The organisation added: "Kick It Out has sought clarity from Romelu Lukaku on comments made to Sky Sports about Nicolas Anelka and the FA investigation into the 'quenelle' gesture.
"Romelu has clearly stated that he had no intention to support the gesture made by Anelka. The campaign continues to work with Romelu as a 'Next 20' ambassador and will look to guide him, in partnership with community organisations, on the sensitivity of issues covering all forms of discrimination moving forward."
