The No.7 scored the first goal and created the second during Wednesday’s 2-0 Carabao Cup win at Milton Keynes Dons, where he filled in at left-back.
Milner led a side that blended youth and experience and was key, according to Klopp, in ensuring there was no drop in the Reds’ level at Stadium MK.
“Millie is unbelievably important,” the boss said at his pre-Sheffield United press conference. “I said it a couple of times. He is Mr Professional, that’s how it is.
“He is very, very serious in all the things he’s doing but still a funny guy in the dressing room.