Kagawa returned to the German giants following a disappointing two-year spell at Manchester United where he was used sparingly and often played out of position.
Leaving Old Trafford was a big relief for Kagawa - something he has publicly mentioned several times - but the creative midfielder has also failed to star this season back in the Bundesliga.
Dortmund have struggled this campaign and have, at times, even sat bottom of the Bundesliga table.
Kagawa's defensive efforts have been criticised but Klopp said he knows what he gets from the Japan international and added that he took encouragement from the 25-year-old's second-half performance against Anderlecht on Tuesday.
Dortmund drew 1-1 with Anderlecht in the UEFA Champions League - a result that saw them finish on top of Group D.
"Shinji is no warrior in defence, that's for sure. But we didn't buy him to play centre-back," Klopp said.
"He came from a, let's say, a not so fantastic situation from Manchester United, he started well when he got back to Dortmund, but now he isn't playing that great anymore.
"So it's possible that you disappear for a while. A lot of players return to form a little bit quicker.
"I mean, Kagawa's first half performance against Anderlecht wasn't good, but in the second half he improved.
"It's all about building and improving our quality as a team in the few training sessions we have over the next couple of weeks.
"But Kagawa has extraordinary skills. He hasn't lost them."
Dortmund visit the German capital to play Hertha Berlin on Saturday.
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