West Brom's French striker Anelka is facing a minimum five-match ban after being charged over the salute which some people regard as anti-Semitic.
But Belgium forward Lukaku, who is on-loan at Everton, said the gesture should not be "a big deal".
Speaking in a video interview posted on Everton's website and later removed, Lukaku said: "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 distanced themselves from 20-year-old Lukaku's interview, which was conducted after the 1-1 draw at West Brom on Monday.
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.
Anelka has denied the salute was anti-Semitic, but pressure groups have called for him to face significantly more than the minimum five-match ban due to his lack of apology.
Jonathan Arkush, vice-president of the Board of Deputies of British Jews, told Press Association Sport: "I know under the rules that on a first-time offence there is a minimum five-game suspension but I think what he did was sufficiently serious to justify a longer suspension than five matches.
"He has not indicated one bit of remorse or regret or apologised for his actions.
"He has simply said he wouldn't do it again and that is not good enough."
The quenelle has been described as an inverted Nazi salute and was created by French comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism. Anelka is a friend of Dieudonne's and the player has insisted his salute was a gesture of support and aimed at the French establishment.
Mark Gardner of the Community Security Trust, which advises the Jewish community on security and anti-Semitism, said the FA should take action against Anelka.
He said: "Anelka has introduced a very ugly phenomenon into British football. Anelka's action risks the 'quenelle' being taken up by actual anti-Semites and used against British Jews: as it has been in France and elsewhere. The FA should throw the book at him."