The Premier League champions were dominant throughout against their League One opponents and comfortably progressed to the Carabao Cup fourth round despite a host of changes.
Liverpool now face Arsenal twice in quick succession, on Monday night in the Premier League and soon after in the cup.
The manager was delighted with Minamino’s application as he showed the endeavour and quality required to fill the role usually occupied by Roberto Firmino, with a brace of goals his reward, and Klopp suggested that central spaces are where he will always be most valuable to the team going forward.
"I loved Taki's game tonight; it was absolutely outstanding and he was involved in so many situations," the manager said after the match.
"More and more, I think we all realise where his qualities are. Wherever he will play in the end, he will end up in the centre.
"If he plays on the left wing or the right wing, he will play in the half-spaces or the centre because that's where he has his real strength.
"The opponent had to kick off seven times [after Liverpool's goals] and the first guy who chased the opponent again when they received the pass was Taki.
"He set the rhythm for all these pressing and counter-pressing situations, so I really, really liked his game tonight."
Minamino scored his first Reds goal in the Community Shield against Arsenal, but has only made one brief sub appearance in the champions’ first two league matches of the season.