The Japan international is hoping to make a bigger impact in the tournament next season after watching his former club make it to Saturday's big match at Wembley
The German side take on rivals Bayern Munich at Wembley on Saturday evening and the Japan international, who swapped Signal Iduna Park for Old Trafford last summer, wants to up his game in Europe next year to follow their example.
"I want to play better in the Champions League next season because I've been inspired to see Dortmund make it to the final," Kagawa told the club's official website.
"I was encouraged to know there is a chance for me to be on the big stage with United.
"I've followed how they are doing and have kept in touch with some of the players. Each time they progressed in the Champions League, I sent them a text to say congratulations.
"Bayern will find it hard against Dortmund as they haven’t beaten them in the league for three seasons," the 24-year-old observed. "Dortmund will play hard without being over-confident.
"I expect it will be an exciting match and I hope Dortmund will be European champions."
Kagawa spent two seasons as a BVB player, having joined from Cerezo Osaka in 2010.