Saturday's 1-0 home victory over Spurs saw striker Lukaku fail to score for a fifth successive game but he did set up substitute Anthony Martial's 81st-minute winner, moments after hitting the post with a header.
The Belgian striker has netted 11 goals for the club this season and Mourinho questioned the home support's treatment of the £75m man.
"I would like the supporters to explain to me why they don't support him so much because he gives everything," he told MUTV. I think it is not fair when scoring the goal or not scoring the goal makes the whole difference.
"I don't think it is fair at all. So, I'm a bit disappointed - but not with him. With him (I am) very pleased."
As well as the reactions from the crowd to Lukaku's performance that irked him, Mourinho also heard some jeers around Old Trafford on Saturday greeting his decision to replace Marcus Rashford with Martial in the 70th minute.
At the final whistle the manager held a finger to his lips as he looked directly into a television camera.
He later said in his post-match press conference when asked about the gesture: "Some people speak too much...calm down, relax." And he added: "Enjoy the football. Don't be speaking all the time so much, anticipating scenarios, trying to put pressure on people. Relax and enjoy football."
Regarding the negative reaction to his substitution from some supporters, Mourinho said: "They pay (for) the ticket, they can do what they want. They can boo a player that doesn't deserve to be booed, they can boo a player that is working like an animal and because the game is not going in his direction.
"They pay (for) their tickets, they can do what they want. They can boo the manager. They can do what they want. There is no problem for me."
Mourinho was full of praise for his team after what was a return to winning ways in the Premier League for second-placed United following the 0-0 draw at Liverpool and the 2-1 loss at Huddersfield.
Having been critical of his players after the defeat at the John Smith's Stadium, the Portuguese said of the game against third-placed Spurs: "If the result is 0-0 or 1-1, my feelings with the players would be the same.
"They gave everything, every ball was like the most important ball of their career. The focus and concentration was there against a quality team. We played well. To play well against a very good team feels even better."
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