Lukaku, the 20-year-old Belgium striker who is on loan at Everton from Chelsea, featured in a video interview posted on the Toffees' website in which he said there did not have to be ''such a big deal'' made about Anelka's controversial 'quenelle' celebration and that he thought the West Brom frontman should not be banned over it.
The quenelle, a pose Anelka struck after scoring against West Ham on December 28, has been labelled anti-Semitic and an inverted Nazi salute, and Anelka must respond to a Football Association charge concerning his demonstration of it by 6pm on Thursday.
Lukaku said in a statement: "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."
The statement was issued through anti-discrimination group Kick It Out, for whom Lukaku is an ambassador.
Reports had suggested he faced being dropped from that role as a result of the interview.
And alongside the Lukaku statement, Kick It Out also on Thursday issued one from the group, saying: "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 (the interview that appeared on Everton's website).
"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."
Lukaku added in his statement: "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 quenelle was created by French comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism.
Former France international Anelka is a friend of Dieudonne's and the 34-year-old player has insisted his salute was a gesture aimed at the French establishment.
On Tuesday Anelka was charged by the FA with making an "abusive and/or indecent and/or insulting and/or improper" gesture, with it being alleged that it was an aggravated breach, in that it included ''a reference to ethnic origin and/or race and/or religion or belief''.
Under new FA rules, such aggravated offences carry a minimum five-game suspension and possibly a longer one.
Anelka, who denies wrongdoing, appears certain to contest the charge as he insists he is neither anti-Semitic nor racist.
Speaking before Anelka was charged, Lukaku said in the interview posted on evertontv: ''He was my idol as a kid and he still is.
''I don't think he should be banned for that, he was just supporting a comedian in France. We don't have to make such a big deal about it.
''I hope he doesn't get suspended because he is a player people want to play on the pitch.''
Everton removed the footage of the interview, which was filmed after the Toffees' 1-1 draw at West Brom on Monday, from their website.
And when asked on Thursday if he had spoken to Lukaku - who joined Chelsea when Anelka was at the London club - about the matter, Everton boss Roberto Martinez said: ''We always speak and obviously this is an important issue because there has been a lot of misunderstanding about it.
''Rom is only a young man and sometimes after playing a game, the emotions could still be high.
''All he wanted to present was a bit of support for a player he has admired from a young age. But he never supported his views or the meaning of those views.
''Remember, there has been a big, big misunderstanding about this issue and the quicker that that gets solved - and it is not for us to solve it, that is for the player (Anelka) and the FA - the better. Everyone will have clarity.
''I'm sure there has been a big misunderstanding. One thing is supporting an individual and something else is to support a gesture.
''Romelu wanted to support an ex-team-mate. He understands there has been a big misunderstanding.
''He has never supported any sort of conflicting views that could be disrespectful to anyone - it is not the type of person he is.''