The France star was named skipper for his side's 2-1 victory over Leicester City on Friday and delivered a commanding performance, which included a goal from the penalty spot.
Pogba was overlooked as the permanent successor to Michael Carrick as club captain, with Valencia instead getting the nod from manager Jose Mourinho – a decision that reportedly upset the midfielder.
The relationship between Pogba and Mourinho is believed to have been strained for some months and the player himself suggested as much when he claimed he would be fined if he said what he wanted to after the Leicester match.
However, when it comes to being a leader in the United team, Pogba says he does not need the armband in order to assume such responsibilities.
"When I was first at United, Rio Ferdinand was captain and Patrice Evra, too," he said. "Then I went to Juventus and Giorgio Chiellini was a captain, [Gianluigi] Buffon was a captain.
"When I was younger, Michael Carrick was sometimes a captain as well. I learned from all of them, but I don't think, being in leadership, there is a book how to become one.
"It's not just about having the armband. I have always been talking to my team-mates.
"It's not a role that I give to myself. I just try to help the team as much as possible, like they helped me, too."
Pogba described it as a "dream" to captain United at Old Trafford, nine years on from first joining the club's youth system from Le Havre.
"I always love this club. I love the club," said the 25-year-old. "I came in the academy, I grew up, I played for the first team. For me, it was a dream come true.
"And wearing this armband, it's even more [special] because of the past, because of the players that played here, the people that have been wearing this.
"It's obviously an honour for me. When I have this, I have the confidence of the fans.
"They're all here, they help me, my team-mates, obviously it makes me want to give them love and give them good performances on the pitch.”