Ole Gunnar Solskjaer's side remain fifth following the victory at Selhurst Park, but they are within a point of Chelsea in third, and level on points with fourth-placed Leicester, who they visit in a final-day showdown.
"There is a positive pressure on us and we want to win the last three games," Pogba told BT Sport before helping United beat Palace.
"We want to win the Europa League, the FA Cup. Last year we didn't win any trophies and I felt empty. We just have to keep working to get there."