The Red Devils got their hands on the EFL Cup and the Europa League last season, but have not won the Premier League since 2013.
In addition, a lowly sixth-place finish in the league and a FA Cup quarter-final exit in the previous campaign suggests that United still have work to do.
However Pogba insists that, with the club back in the Champions League, having qualified as Europa League winners, they can build on last season and get back to the "big Manchester United" of old.
"What's a good season? Winning everything! We are Manchester United and we want to get back to being the big Manchester United," he told Sky Sports News.
"We want to win more trophies and do better in the Premier League and we're obviously happy to be back in the Champions League. We're here to do great things.
"Do I have to be more of a leader? No, I'm just myself. I'm the same, talking, encouraging players. I'm 24 now but when you are on the pitch there is no age.
"When I was young I was doing the same. A good season for me? Winning everything! A player has a great season when the team does great. That's it."
Jose Mourinho's charges get their Premier League campaign underway on Sunday with a home fixture against West Ham United.