The midfielder inspired France to a winning campaign in Russia, defeating Croatia 4-2 in the final.
Leicester was taken to the sword last night in the first game of the Premier League of the United States with Pogba playing an influential role.
Manager José Mourinho selected the £ 89m signing despite his lack of preseason after a post-World Cup break.
But the 25-year-old did not show signs of rust, scoring from the penalty spot after three minutes in a good display.
After winning the Europa League, League Cup and Community Shield in the first season of Mourinho, United was without a trophy the last time.
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"That [the World Cup] it's in the past, it's part of the story "
Manchester United star Paul Pogba
Pogba spoke after the 2-1 victory over the Foxes, which saw Luke Shaw grab his first high-level goal, signaling he wants more cutlery with his club.
"I will not be full of a World Cup," said Pogba Sky Sports following the game
"I know it's a great cup, it will stay in my mind, but I want to win all the trophies.
"I have not won the Premier League, I have not won the Champions League, I have not won the Euros, so there is more to win."
"That [the World Cup] It's in the past, it's part of the story. I am someone who likes challenges and wants to progress and you should leave it behind now.
"You have to keep that in mind, but you have to keep working to improve more and more because I'm still quite young.
"I want to progress and improve again and I want to win more trophies.
"We should start the Premier League with a victory and we did it today.
"We knew it was going to be difficult because some of us, including myself, did not have any pre-season games."