Kagawa has yet to fully bounce back from a serious injury sustained while on international duty with Japan at the Asian Cup in January, and has struggled to recapture the form that saw him hailed as one of the Bundesliga's most exciting talents last season.
While he has appeared nine times for Dortmund so far this season, he has looked a shadow of his former self and only recently admitted he was struggling mentally.
However, he bagged two goals for Japan in their 2014 World Cup qualifier against Tajikistan on Tuesday, and is hoping to build on that performance to once again shine for Dortmund.
"I want to use this as a springboard and produce results as I know that will definitely lift me up both condition-wise and from a psychological point of view," Kagawa told Kyodo News.
"Obviously psychologically this is a relief and I was pleased with my first goal. I have achieved something big and I am delighted that I will be able to go back [to Dortmund] in a positive frame of mind.
"I made some simple mistakes in midfield and I have to improve my accuracy as the qualifiers will get tougher now that we are going to be on the road."
Japan coach Alberto Zaccheroni was effusive in his praise of Kagawa's performance on Tuesday night, in a game which also saw Stuttgart forward Shinji Okazaki and Ventforet Kofu rookie Mike Havenaar bag braces.
"I'm pleased with Kagawa's goals and the result, but the thing that pleases me most is the way he increased his movement off the ball compared with the last game.
"He can play on the wing or in the central attacking position and he gets in the box, and I'm fully aware what an important player he is for us. He scored and had a great game."
Kagawa's brace on Tuesday brings his tally to nine international goals in 27 caps for the Samurai Blue.