The Belgium forward 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 the West Brom player's actions.
However, with comment growing on social media, Everton removed the footage when they became aware there was an issue.
"It is the player's opinion and not the opinion held by the football club," Everton's director of communications Alan Myers told Press Association Sport.
"We moved quickly to remove any interview that may have been offensive to anyone.
"The last thing we want to do is cause offence to anyone."
Press Association Sport understands, due to the way the website is managed in collaboration with external partners, the interview from the post-match mixed zone after Everton's 1-1 draw at West Brom was conducted by another media organisation and uploaded without anyone at the club initially being fully aware of its content.
Everton have yet to speak to Lukaku, who is an ambassador for football's anti-discrimination group Kick It Out, about what he said but it is believed the striker's relatively young age - he is 20 - and friendship with Anelka will be taken into consideration.
There is no suggestion the striker will be disciplined as a result of his comments.
On Tuesday Anelka was charged by the Football Association with making an improper gesture and 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-match ban and possibly a longer suspension.
Speaking after Monday's game and before Anelka was charged, Lukaku - who knows the Frenchman from their time together at Chelsea - 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."