Kagawa joined from Borussia Dortmund a year ago and finished the season with a Premier League winners' medal but a knee injury mid-campaign meant he was only intermittently a regular starter.
"It was great to win the title with United," Kagawa told Inside United. "But I feel I still have work to do. I would say I am half satisfied, half unsatisfied."
The 24-year-old has won three league titles in a row having claimed back-to-back Bundesliga crowns with Dortmund before moving to Old Trafford.
He played a pivotal role in the Dortmund attack but has not enjoyed the same impact at United, although he still expects to prove his worth.
"You have to believe in yourself," he said. "If you don't, things can go wrong both on and off the pitch. Being positive and believing in yourself is important, not only in football but also in improving as a person."
Sometimes last season he was picked above Wayne Rooney, but Kagawa is hopeful the England international will remain at Old Trafford and rekindle a successful partnership with Robin van Persie that wreaked havoc in opposition defences at the start of last season.
"It is inspiring and exciting to play alongside such world class players," said the Japanese international.
"Wayne can do everything to the highest standard. He has everything a football player would need: team spirit, hard work, switching between attack and defence.
"You don't see such players very often. He plays for the team, plus he can score and assist. There is so much I can learn from him and I enjoy playing with him. Robin, of course, made the difference with his goals. He's wonderful."