The Belgian international, who joined the club in a £75m deal from Everton, was on target in United's 2-1 friendly win over pre-season opponents Real Salt Lake in Utah.
Leading up to the goal, Mourinho spoke to Lukaku on the touchline to tell him that scoring at this stage is "not important", and he was full of praise for the 24-year-old striker.
"I think it's just nice for him but not important for me," the manager told reporters. "When he came [over to the touchline] for the water, before he scored the goal, I told him, 'I love everything you do on the pitch. Don't be worried about scoring or not scoring because it's not important.'
"He holds the ball so well, he plays one touch, two touches so well. He sees, he moves, he gets behind people, he attacks crosses, he works with the team and when we lose the ball he presses well. I like everything he does.
"For me, it's easy to feel it because he was my player four years ago or something like that, his evolution was great. He's now a top striker and the goal is just a detail, not important."
Lukaku scored 25 Premier League goals for Everton last season.