"I understand the reasons we did not start the game very well, why did we take 20-25 minutes to be in control," says Mourinho.
"They know how hard it is that the opponents play on this tent, they are forced a little and they create some problems, but the goal changed everything and after that we agreed and it was nice to start the victory."  By Pogba's achievement, the boss added: "If he starts coming into possible points positions that may be a plus for the team, I'm happy with that."
Really a club in crisis at the end of August after his 3-0 home defeat against Tottenham Hotspur, it was United's third straight victory since then, all from home.
Tougher tests are expected in Group H, but with Valencia because of Old Trafford for two weeks, and Juventus is following it.
"I'm pleased with the team's solid solid performance more than any individual," added Mourinho.
"We know we needed to win this match, we knew it was very important to go to the next three matches against Valencia and Juventus twice with these three points."
There were many reasons to be careful about this trip, with United having lost to Basel on their last two visits to Switzerland.
The surface here was considered to be an adequate danger to Mourinho for leaving Antonio Valencia from his group. This meant a debut for Portuguese teenager Diogo Dalot, signed in the nearest season from FC Porto.
"For Diogo, the first match for the club after knee surgery, I think a very solid performance, everyone can see the potential, he is a 1
This was a great opportunity for young boys, Swiss champions last season for the first time since 1986 and making their Champions League group play debut.
They were driven by an electrical atmosphere generated by a crowd of over 31,000 and was the better team for 35 minutes.
With the Swiss star Kevin Mbabu who featured the right back, the hosts saw Guillaume Hoarau head right next to it, while Mohamed Ali Camara and Christian Fassnacht both tested David de Gea from intervals.
Marcus Rashford hit the outside of the post but the visitors offered a bit until Pogba gave a moment of magic 10 minutes before integrating rval.
Superb footwork on the edge of the box put him in front of goalkeeper David Von Ballmoos and hit the net. He had his first Champions League goal since returning to Old Trafford in 2016, and it dampened the lively home support.
Still, Young Boys had a battle chance if they had gone on just one behind the range. But the German referee Deniz Aytekin's decision to give United a penalty two minutes before the break effectively killed the game.
Luke Shaw's cross hit Mbabu's arm from close range. It was a difficult conversation, and Pogba duly converted the spot-high.
"It was quite difficult for us. The referee could have decided for the other way," said Young Boys coach Gerardo Seoane. "There was no intention from the player and it was a crucial moment in the game."
Pogba was then the architect for the third goal of the visitor halfway through the second half with a driving run and passed for Martial, marking his first start of a month by striking Von Ballmoos with the help of a slight bend.