The league leaders were made to work hard for all three points, with the winner arriving twenty minutes to full time when Blades goalkeeper Dean Henderson allowed Georginio Wijnaldum’s tame volley to go through his legs.
The win takes Liverpool eight points clear of Manchester City for the time being with the champions yet to honour their fixture away to Everton later in the day.
"These games, they are not all beauties and you have to work hard for the result," Klopp told BT Sport.
"You have to respect the opponent. We had good moments and it was one of these games you have to win but not think too much about it. One team deserved to win, which was us, but all respect to Sheffield United; they were tough.
"I was frustrated and at half-time we spoke about it. We started well, but you have to do the same things again and again. It's about body language. It starts with the centre-halves; it's the little things.
"They threw everything at us and they worked incredibly hard. They were a real threat.
"I am fine with the game; not overly happy but it happens. We were concentrated at set pieces for 95 minutes; the boys were spot on. We didn't play our best football but there we are."
Liverpool are back in action on Wednesday against Red Bull Salzburg in the Champions League before hosting Leicester City in their next Premier League game.
