Martinez, who worked with Lukaku during the pair’s time at Everton as well as the national team, says the 24-year-old’s trust in his own abilities will not have been affected by the criticism he’s attracted.
"For me nothing has changed in Romelu's mind. He is confident, he has an incredible belief in what he can bring,” Martinez said.
"All I want is that he carries on seeing himself in that manner when he scores and when he doesn't, which is going to be highlighted in a club like Manchester United.
"I've got a big advantage with Romelu because I've worked with him for four years… I know Romelu inside out.
“I think he just relishes the challenge. He's been enjoying a really good start to the season and now is a period he is ready to cope with.
"I have no worries whatsoever. All he needs to do in his career is to carry on being himself in a club with the expectations and the demand of Manchester United.”
Fellaini featured as a substitute in United’s 1-0 defeat at Chelsea on Sunday after nearly a month on the sidelines and Martinez believes it was not worth the risk in playing the midfielder.
"He needs a proper 10 days’ work with no game in order for him to be fully fit," he said.
"Medically it is the right choice to allow Marouane to get fit. If it had been a competitive game I think we would have called him up because maybe for the second game, he could have been on the pitch.
"This is a period where we can afford not to risk him until he is 100 per cent."