Rosenborg created the better chances throughout the contest and incredibly hit the woodwork on four separate occasions before Noah Emmanuel Jean Holm struck the winner in the 93rd minute.
Man United only had five senior squad members in their travelling party, with Jonny Evans, Aaron Wan-Bissaka, Mason Mount, Casemiro and Marcus Rashford starting for the 20-time English champions.
There were new faces in the dug-out, meanwhile, with Rene Hake, Jelle ten Rouwelaar and Ruud van Nistelrooy all present alongside manager Erik ten Hag, and the team also sported their new home kit for the first time.
Here, Sports Mole picks out three talking points from Man United's opening game of the summer, with their attention now set to turn to another friendly with Rangers on Saturday.
Man of the Match Vitek puts in excellent performance
Radek Vitek was comfortably Man United's best player on Monday, with the 20-year-old goalkeeper putting in a man-of-the-match performance between the sticks.
The 6ft 6in stopper spent the second half of last season on loan at Accrington Stanley in League Two, making 18 league appearances, and he is now back with the Red Devils this summer.
Vitek will certainly have given head coach Erik ten Hag plenty to think about with his display, as he made a whole host of smart stops against the Norwegian outfit.
The youngster was also impressive on the ball and continued to take up good positions, and it would not be a shock to see him form part of the first-team goalkeeping group next term if he continues to make a strong impression during the team's pre-season preparations.
Rashford disappoints in 45-minute outing against Rosenborg
There remains huge speculation surrounding Rashford's future, but it would be a surprise to see him leave the 20-time English champions during this summer's transfer window.
Having been left out of the England squad for Euro 2024, he was available for this match, starting down the left, but the attacker failed to make a positive impression.
He was overshadowed by Ethan Wheatley in the opening half of action, and there is no getting away from the fact that the 2024-25 campaign is a huge season for the Red Devils academy product.
Not too much should be read into the defeat to Rosenborg, but the club's senior players failed to make their mark, with Casemiro, who is being linked with a switch to Saudi Arabia, also underwhelming.
Casemiro was on the end of a poor challenge in the first period, but Ten Hag said after the match that he is expecting the Brazilian to be able to train on Tuesday.
Ten Hag critical of Man United performance
Ten Hag was critical of the Man United display on Monday, with the Dutchman admitting that he expected to see more from his players in their first pre-season fixture.
"The result is not secondary," Ten Hag told MUTV. "Of course, we play pre-season but at Man United the standard is you win games and definitely don't lose games.
"So if you can't win, don't lose the game, like we did in the last second of the game. But of course, the performance is more important and the performance was below standards.
"Let's say he (Vitek) got the opportunity from the team to make some very good saves because the performance from the team is, by far, not good enough.
"We can talk [about] everything that is bad, but I'm not that guy. I have seen and this is not the standard for top football. Top football, you have to achieve much higher standards, starts with any individual, make sure you're fit.
"I know we can't be match-fit in this moment, I know you need these games. The opponent is in the league, they have a much higher fitness level but we are Man United and players from Man United, a team from Man United, should perform better."
What next for Man United?
Man United will continue their pre-season with a clash against Rangers on Saturday afternoon, before heading to the United States for games against Arsenal, Real Betis and Liverpool.
The Red Devils will then tackle Manchester City in the Community Shield on August 10, with their first Premier League match of the 2024-25 campaign coming six days later against Fulham.