The 24-year-old put the Red Devils ahead seven minutes before the interval in the 2-1 pre-season friendly victory, rounding the goalkeeper and rolling the ball into an empty net at the Rio Tinto Stadium.
Lukaku, who made his United bow in the 5-2 win over Los Angeles Galaxy at the weekend, hopes to build on his first strike after quickly settling into his new surroundings.
"Obviously, I'm here to score goals and be a focal point for the team," he told MUTV. "At Manchester United, we play to win. That's my first mentality when I get onto the pitch. Then everything else comes with it. I feel really well. Pre-season has been going really well for us.
"We've been working really well to prepare for the season ahead. The competition is there. Everyone is working hard to have a place in the team. I'm delighted with another win for the team. We did well and we need to keep improving because now we are playing better opponents and we need to improve.
"This is what the manager wants, to play attractive football. Hopefully we will be prepared and ready to do the job. I know a lot of the lads, a lot of them are neighbours so I didn't take time to settle in. I have been waiting for this opportunity, now I am here and it is time to work hard."
Lukaku cost United an initial sum of £75m to recruit from Everton, making him the most expensive Premier League signing of the summer transfer window so far.