Former Old Trafford favourite Solskjaer -- known in his playing days as the "Baby-faced Assassin", has been appointed as caretaker manager until the end of the season after Mourinho was sacked earlier this week.
The Norwegian, 45, who spent nearly 15 years with United as a player and reserve team coach, has stressed the importance of his stars playing with a smile on their faces under his leadership after a miserable season so far.
But he also said he would not be afraid to take a leaf out of the disciplinary book of his former United manager and mentor Alex Ferguson, whose legendary temper tantrums became known as the "hairdryer" treatment.
"We are all different to how we manage people and the manager (Ferguson) was different to every individual," said Solskjaer.
"Of course, maybe I should get the hairdryer out of my pocket because I've got a hairdryer -- when my hair needs lifting I use it on myself. But I am also not afraid of, if you like, laying down the law.
"You know with your kids when they disappoint you, you tell them off, you don't give them some chocolate do you?
"So you treat players similar to how you treat your kids really because you want the best for them, you want to guide them, you want to help them."
Solskjaer's promotion from Norwegian club Molde, who have "loaned" him to United, has surprised many in football.
But he has been a popular appointment, not least because he has worked with a number of the club's current players in his previous coaching role.
Pogba, whose relationship with Mourinho had been little short of toxic this season, was a member of Solskjaer's reserve team in 2010 and the interim boss has pledged to try and return him to the form he showed in helping France win the World Cup.
"He's a World Cup winner," said Solskjaer. "Paul is a terrific lad and when I had him as a kid, he was always there, the happy-go-lucky lad.
"He hasn't changed personality-wise. He's a better player of course and he's one that I want to get the best out of. You have so many quality players that I want to get the best out of. He's no different to anyone else in that respect."
While Pogba's new manager dismisses the argument that the balance of power in football clubs has shifted to the players, he has reminded the Frenchman, and others, about their responsibilities with regards to social media.
Pogba quickly deleted a controversial social media post of him smiling after manager Mourinho was sacked.
"I'm not sure about you saying the power has gone to the dressing room," he said. "Football has evolved, of course, and the gaffer (Ferguson) was in charge of more or less the whole club.
"Football is developing. The structure of the club has developed. The power is with the manager. He picks the team, the tactics, the strategy.
"The philosophy is in these walls. That legacy is more important than any player power. I have to say being a Man United player is a privilege and I think all of them want to succeed here."
Solskjaer's first game in charge will be at his former club Cardiff although he appears likely to be without forward Romelu Lukaku, who has been absent from the club this week, attending to a personal matter.