Pogba opened the scoring with a deflected shot in the 18th minute, before Henrikh Mkhitaryan put the match to bed early in the second half.
United's success comes just two days after the terror attack that claimed 22 lives at Manchester Arena and Pogba said his team-mates wanted to win to honour the victims
"These things are terrible all over the world, in London and in Paris," Pogba told BT Sport.
"We went out focused to win and we won for Manchester and the country."
United had to settle for sixth place in the Premier League table following a difficult season, but the victory in Stockholm saw United lift a third trophy this season after their Community Shield and EFL Cup successes.
"We did it. We are very proud. Nobody can talk," Pogba added.
"They said we had a bad season but we have three trophies.
"The start was important and after the goals we controlled the game.
"It was a great performance from everybody in the team."