The below-par Reds successfully negotiated a tricky test against a rock-bottom Blades team boosted by the return of Chris Wilder to the Bramall Lane dugout on Wednesday night following the dismissal of Paul Heckingbottom.
Captain Virgil van Dijk's first-half volley and midfielder Dominik Szoboszlai's late finish secured a hard-fought 2-0 victory that kept them second in the table and cut title rivals Arsenal's lead at the summit back down to two points after the Gunners sealed a dramatic last-gasp triumph at Luton on Tuesday evening.
But despite that win Klopp was evidently in no joking mood, labelling Amazon Prime host Marcus Buckland "completely ignorant" for a light quip he made during a post-match interview about Liverpool now getting the manager's "favourite kick-off time" when they head to Selhurst Park to play Crystal Palace on Saturday lunchtime.
"That's brave, I have to say. That's really brave to make a joke about that, really," said Klopp, long an outspoken critic of the Premier League's fixture scheduling - particularly early weekend kick-offs that follow midweek action.
He then added: "It is constant. We go home, I don't know exactly what time we will get home, we will arrive, maybe 1am-2am tonight and then we play again. We have two [training] sessions.
"It is fine to recover and then we go again. Crystal Palace play tonight as well [at home to Bournemouth] so it is absolutely fine.
"I realise you don't understand it as well even when you work in football, so why should I try to explain again.
"If you make a joke out of that you are completely ignorant. But it's good, football is entertainment and I understand. It's all good."
Buckland quickly insisted that he did not mean to be disrespectful, but Klopp did not back down in the awkward row.
"You were already," he said. "All good, you can say what you want, I cannot say what I want because that would be really different."