Pogba, 25, has been under severe scrutiny from manager Jose Mourinho and English press for his performances in the Premier League this season.
And the France international concedes, winning the 2018 FIFA World Cup was a huge contributor to his inconsistencies.
"It's hard to concentrate, to start again, to hit hard, because we touched the stars," he told AFP. "For us, it was the best trophy you can win as a footballer.
"But we like challenges too, we have goals. For example, I've never won the Premier League, that's an objective. I'd like to do that."
Mourinho revealed in September that Pogba would no longer lead the side in the wake of his post-match comments questioning his tactics in the 1-1 draw with Wolves.
This after the former Juventus superstar was credited for his incredible leadership abilities and inspirational team talks with Les Blues in Russia.
And the eccentric midfielder has now broken silence over Mourinho's claims that he has no qualities to lead the Red Devils.
"I've never played for the France team to be captain, already being here is a big thing for me," Pogba said. "You don't have to be captain to speak.
"For me, a leader isn't someone who wears something on his arm, who puts on the captain's armband.
"It's the squad that put me in that position, who gave me the freedom to express myself, and gave me the confidence to."