United are outsiders to claim Champions League qualification via domestic football though they remain in contention, four points adrift of fourth-placed Liverpool with a game in hand ahead of Monday morning's AEST trip to Arsenal.
The UEFA Europa League, where United lead Celta Vigo 1-0 in the semi-finals, looms as the club's best chance of returning to the illustrious competition.
Pogba, however, is adamant United – on a 25-match unbeaten run – are more than capable of finishing in the top four.
"Of course, we have to believe," Pogba told MUTV.
"Obviously, we want to do it and we can. Of course we're strong enough, we are Manchester United and we can do this.
"To be in the top four, our mind has to go there, and we also want to win the Europa League. We have to keep our heads on the challenge and the big objective; we want to achieve the big goals, not the small ones.
"We're confident of that. We're young and fresh."