Klopp was forced to bring on the Japanese international forward in the first half at Molineux on Thursday night after Sadio Mane picked up an injury.
Minamino played the rest of the match from 33 minutes onwards, but was suffering an injury of his own, according to his manager Klopp.
"It was really difficult for Taki," said the Liverpool boss, when asked for his verdict on Minamino's Premier League debut.
"He felt immediately his calf, he needed treatment at half-time. That was, for his first Premier League game, exceptional."
Klopp also provided an update on Mane's situation after the match, admitting he may miss Liverpool's next Premier League clash against West Ham.
"Sadio is a real shame he had to go off," said Klopp. "Hopefully it's not too bad - just a muscle tweak, but we will see tomorrow."