The Japan international played in both positions at the Anoeta but has reiterated that he is far more comfortable being utilised as a trequartista
The Japan international started the Champions League game out wide but moved into a No.10 role in the second half, a position which, he admits, he found far more preferable.
"I had an easier time playing as a shadow top [trequartista] than I did on the left wing," Kagawa told reporters.
"I need to be more involved in the match and I hope I can do so in our upcoming fixtures. I want to play better, sharper and faster."
The Premier League champions had chances to win the game, with Robin van Persie twice hitting the woodwork, but ultimately had to settle for a point.
The draw means the Red Devils still top of Group A but they remain just a point clear of Bayer Leverkusen, and Kagawa feels that his team might have done even better and secured all three points.
"I think it was a game we could have won," he added. "If you look at the other groups, too, the number of points you earn in games like these can decide whether or not you advance.
"If we could have converted our chances, we could have won."
Kagawa also insisted that little has changed at the club despite Sir Alex Ferguson leaving Old Trafford after almost 27 years in charge and David Moyes taking over at the helm.
"I don't feel like there are any big differences," he claimed. "Their instructions change from match to match, after all."