But they hit back impressively in the second half, with Marcus Rashford and Harry Maguire hauling them level before Cristiano Ronaldo headed the late winner.
Coming just days after a dismal 4-2 defeat at Leicester in the Premier League, midfielder Pogba said the spirited comeback showed his team's character.
"We showed big character, the character of this team, of this club," Pogba told MUTV.
"It was a very good result even if we didn't start well but at the end we got the result that we wanted and the energy, you could feel the belief and the positive energy just on the pitch.
"I can say it was a beautiful win, with the belief, we kept believing."
Solskjaer's side have lost two in a three-game winless streak in the Premier League.
France World Cup winner Pogba said something needed to change after the Leicester loss.
Asked if he saw a positive difference on Wednesday, he said: "On this game for sure the energy is more positive.
"But then when you say change it doesn't mean like you will change straight away. It's a work (in progress).
"It's all of us, it's a trust with everyone. It's a belief and you stick together, so all this is coming game by game but today for sure it's a big reaction.
"It's the way that we have to carry on until the end of the season."
United face bitter rivals Liverpool at Old Trafford on Sunday, with Tottenham and Manchester City also on the fixture list before November's international break.
"I mean, that's the beauty also of football because it's not a game that you can say 'oh, you rest'," Pogba said.
"You have to go again. We knew that it will come anyway, big teams, big clubs.
"We're Manchester United, we know it's not going to be easy but we're here to play those games."