The Japanese attacking midfielder was a bright spot for his squad, salvaging some pride in stoppage time with his first goal in Europe's most elite club competition.
"I didn't think they'd get the better of us but perhaps we started out on the wrong foot," Kagawa told reporters after the match.
Dortmund lacked their free-flowing cutting edge on Wednesday night, and the midfielder blamed his team's poor pace on injuries to Mario Gotze and Sven Bender, both of whom were substituted before the half-hour mark.
"Because we had those injuries, to some extent we couldn't get a rhythm started," he added.
"I thought that if I turned well I wouldn't have the ball taken. I didn't think there was that much pressure, but when I had possession everyone's reactions off the ball seemed a bit slow," the 22-year-old said.
"When Arsenal's players came close to me they were able to exert their strength, [Alex] Song in particular."
When asked about his goal, he found little difference between the 2-0 result that could have been and the 2-1 result that was.
"If you just look at the result zero and one are different, but I don't know, I'm not exactly jumping for joy about [the goal]."
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