The Reds went second in the Premier League after mounting a comeback against the Blades.
Sander Berge scored early on from a controversial penalty at Anfield as the home side toiled.
Roberto Firmino equalised before half-time and Liverpool took charge after the break.
Summer signing Diogo Jota got the winner just after the hour mark after some fine work from Sadio Mane.
Merseyside rivals Everton are the ones keeping Liverpool off the top spot on goal difference at the moment.
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But Klopp was still not fully impressed with his strikeforce, lamenting a lack of balance.
He said: “We were a bit too hectic at the start. We had four offensive players on the pitch but all offered the same option.
“But I love half time. The second half started good and for 20 to 25 minutes we were really good.
“We could have scored more and then they came back.
“We had to dig deep but the boys did.
“It’s nice to win 2-0 or 3-0 every game but that only happens if, in games like this, we are ready to fight hard.
“On nights like this you earn the right to win the others like that.
“Really good partnership at the back, but they have a tough job to do.
“The penalty conceded was clear it was a challenge to win the ball.
“We are on the wrong end of another decision, but luckily we could sort that tonight, so maybe I should not talk too much about that.”
There is no time for rest during this period of the season, with a Champions League match coming up next against FC Midtjylland on Tuesday.