The Japan star did emerge from his debut campaign with a Premier League title winners' medal.
He also bagged a superb hat-trick in a late season victory over Norwich.
However, a major knee injury halted what had been an encouraging start to life with United, and the former Borussia Dortmund star never quite regained his form of old.
"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."
After taking on a pivotal role in the Dortmund outfit that won back-to-back German titles, then reached the Champions League final last term after Kagawa's exit, the 24-year-old has no doubts about his ability to carry out the job.
"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."
Should Rooney remain within the Red Devils fold, as Moyes hopes, the competition for Kagawa would remain huge, with Robin van Persie, Javier Hernandez and Danny Welbeck also vying for advanced roles beyond the midfield.