The Borussia Dortmund coach praised the performance of his Armenian ace against Napoli and warns there will be more to come from the summer signing
The 24-year-old has endured a mixed start to his career at Signal Iduna Park following a £22.8 million (€27.5m) summer switch from Shakhtar Donetsk.
However, Mkhitaryan sprang into life with an impressive display against Rafa Benitez's men, creating a host of opportunities and scoring as last season's beaten finalists secured a convincing 3-1 Group F victory to boost their chances of reaching the last 16.
"He was exceptional against Napoli," Klopp, 46, told reporters. "That was his best game for us.
"He is a player who can really make a difference and he can continue to improve. He has settled much quicker than new additions in recent years.
"Ikay Gundogan took half a season to settle and Robert Lewandowski longer than that.
"We must work hard to make sure he can emulate that performance."
Dortmund head into their final Champions League group stage game in two weeks' time knowing that victory will definitely see them reach the knockout stages of the competition.