Last year's champion Shahjalal and runner-up Jibon Boli did not participate in this year's competition
Pogba played in Josh Harrop with a curling through ball in the 15th minute and the 21-year-old cut in from the left to give United the lead with a powerful shot and mark his senior debut with a goal.
Pogba doubled United's lead minutes later after Jesse Lingard drove at Palace's defence before playing a square pass that the Frenchman slotted home after a slip by Joel Ward.
Christian Benteke headed against the post after the interval as Palace ended the season in 14th place. United, who face Ajax Amsterdam in the Europa League final on Wednesday, finished sixth.