The £75million striker played 45 minutes of United’s 5-2 victory over LA Galaxy in their first pre-season friendly.
Lukaku came off the bench at half time with the score at 3-0.
But team-mates Henrikh Mkhitaryan and Anthony Martial got on the scoresheet instead in the second half.
Fellow striker Marcus Rashford bagged an impressive brace in the first half.
And it means Lukaku will have to wait to break his United duck, having missed a couple of good chances against Galaxy.
Romelu Lukaku made his Manchester United debut against LA Galaxy
But Mourinho was quick to defend the former Everton man.
However, it appears the 24-year-old is already following his manager’s tactics and pleasing the Portuguese.
Romelu Lukaku in Manchester United's first training session Mon, July 10, 2017
Click to reveal the best snaps of Romelu Lukaku in Manchester United's first training session of the season
Play slideshow Getty Images 1 of 10
Romelu Lukaku got stuck into Man Utd's first training session of pre-season
He didn’t score goals but he played better than the ones who [did] score goals
Get Quotes on Home Insurance
“He didn’t score goals but he played better than the ones who [did] score goals,” Mourinho told ESPN.
“Target man, hold the ball well, good movement, not selfish, team player, very strong holding the ball and not losing, fast on the counter attack – so happy.”
Lukaku will hope to net his first United goal when they face MLS outfit Real Salt Lake on Tuesday (3am).