The 25-year-old returned to Dortmund a fortnight ago for a reported fee of £6m after spending two years at Old Trafford.
The Japanese midfielder scored on his return to the Bundesliga as Dortmund beat Freiburg 3-1 on Saturday.
"I was kind of surprised Kagawa was on the market again," the Manchester Evening News quotes Klopp as saying.
"His first year at Manchester United was Sir Alex Ferguson's last year, so that isn't the time to develop players. The only thing you want at that stage is results and titles.
"Kagawa's second year at United was the first year of the new coach, so that's also all about results. Then there was a third manager [Louis van Gaal] with a very successful philosophy. So we saw the chance to sign Kagawa and we took it."
Kagawa scored six goals in 57 appearances for United.