Dortmund secured the championship with a 2-0 win over Borussia Monchengladbach, with goals coming from Ivan Perisic and Kagawa.
And having missed the second half of last season's triumph due to an injury sustained while on international duty with Japan, the 23-year-old admits he now feels complete at having played an integral part in a title success.
"I'm feeling a lot of emotions, and I really do feel a sense of completion," he said after the win over Gladbach.
"Even though we had a really difficult period, we were able to win the championship and it's because of how close we all are.
"I really want to thank my team-mates and the fans. This wasn't something I could have ever accomplished alone, and it's amazing."
The Japan international revealed he was delighted to have scored the goal that sealed the title for Dortmund, but admitted it hadn't been easy early on when Gladbach were playing as a compact unit.
"To score a goal like that as we were closing in on winning the championship and guarantee the result was really incredible," he added.
"I had bit of room to work in. In the first half, I didn't feel like I had room when I was moving, but in the second half I felt like I really did.
"Our opponents stopped pressuring us. In a late-season game like this, it's hard for our opponents to stay motivated. But we were motivated by the opportunity to win the championship, and so we were able to create many chances."
Dortmund will be looking to complete the domestic double when they take on Bayern Munich in the DFB-Pokal final.