The Japan international, who was again on the scoresheet, admitted it wasn't easy to win in difficult conditions but was pleased with the way his team played the second half
The Japan international, who scored a brace and assisted Dortmund's fourth goal, wasn't particularly happy with the way his team played the first half, in which the German champions found it difficult to create goalscoring chances.
"It's not them [Koln] being good, it's that we were bad. I wish I'd gotten the ball more, and I was calling for it but it didn't come," he told reporters after the match.
"I thought I'd definitely have an opportunity to create chances in the second half, and I'm glad I was able to convert with a header."
The former Cerezo Osaka man revealed hot conditions didn't help his team in the first half, making player movements slower than usual.
"It was really hot today, so in the first half everyone's movement was a bit slow, and in that our opponents scored first and it was a difficult start," he added.
"I'd like it if we could start more games with the sort of play that we showed in the second half."
Kagawa also admitted that understanding Bayern's result made their match more difficult and that there are many points his team need to improve if they want to win the Bundesliga title.
"Understanding that Bayern had won, and play 90 minutes on the road meant that we knew it would be a really difficult match," he said.
"The result itself may has been a landslide, but if you look at the match as ou performance in the first and second half, there's a lot of points that need to be improved. But right now the most important thing is winning."