Signed from Everton at an initial cost of £75million, the 24-year-old hit the ground running at Old Trafford with 11 goals in his first 10 matches for the club.
The striker has since failed to score in his last five matches, with apparent fan agitation in Saturday's 1-0 win against Tottenham getting under Mourinho's skin.
The United boss said it was unfair that fans 'don't support him so much' as, whether he scores or not, the Belgium international makes a difference - frustrations he repeated ahead of the Champions League clash with Benfica.
"The fans are the fans, and they pay their ticket and are free to express themselves however they want," Mourinho said. "But my job is, when I feel they deserve, to protect my players and I feel Romelu is one of the players that should be untouchable in terms of the respect from everyone.
"It's not one ball that hit the post or one save by the opposite goalkeeper that can make Romelu's contribution below the top level. He's playing extremely well for us and yes, I have to protect my players when I think my players deserve it.
"Romelu always deserves it because of what he does for the team, what he does for the team is fantastic. Playing football for a striker is not just about scoring goals.
"So for me he is untouchable for my team and untouchable also in the support and the respect that he deserves from the fans."
Put to Mourinho that perhaps it is typical of a striker like Lukaku to have quiet moments, he said: "I don't think he's quiet at all.
"Ask (Toby) Alderweireld and (Jan) Vertonghen and (Eric) Dier if he was quiet! And they are some of the best central defenders in football."