Minamino was handed a rare start in Liverpool's Carabao Cup win over Norwich, grabbing a brace at Carrow Road.
Klopp insists the 26-year-old needed time to settle as he looks to manage expectations.
"He is an outstanding talent," said the German. "Everything was difficult when he joined and you need to get used to the Premier League.
It helped massively going to Southampton and he came back a different player and a different package. Players need time."
At St Mary's Minamino made 10 appearances, scoring on two occasions.
lopp accepts that Minamino will want the maximum amount of minutes but has no worries about him going forward.
Klopp said: "Footballers want to play, that's clear. He was with his national team, got injured and was then not fit so it was not like he didn't play for 60 weeks.
"Taki is in a really good moment. Stuff like this is not always easy but he is to character. I really enjoyed his game tonight. It was important for him and for us.
"So yes that will help him and help us. Players need time to get back on track after an injury. He is in a really good moment. He trained really well.
"He deserved his two goals. His first one was really good awareness, quick in mind and finished the situation off.
"The second one I didn't really see 100 per cent but his acceleration into the box and his shot in small space was really good.
"And he was really good in preseason. No body has to worry [about Minamino]."
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