The German made seven changes, including a first start of the campaign for Philippe Coutinho, to the side that was held at home 2-2 by Sevilla in the Champions League in midweek, but yet another defensive error cost Liverpool dearly against a Burnley team that has not won at Anfield in 43 years. However, Sean Dyche's men will be full of confidence and they will head into the fixture on Saturday much fresher than their opponents.
"He delivered a very, very good performance (against Palace) in a tough game, an awkward game for us".
Fortunately their lead didn't last long.
Mohamed Salah swivelled to dispatch a shot past goalkeeper Nick Pope three minutes later, but the seemingly inevitable second never arrived for the hosts.
They were unlucky, perhaps, not to see a late flurry of chances produce a winning goal, but by the final whistle, Anfield regulars were left asking the usual questions.
The home side dominated but were unable to break through again. An innocuous collision with Ben Mee saw Tom Heaton land badly on his shoulder causing a dislocation and meaning he will now be out of action for several months.
The goals opened up what had been a tight affair with Salah, twice, and Sturridge testing Pope with low shots that were comfortably dealt with.
Liverpool have kept four successive league clean sheets at Anfield since the defeat to Crystal Palace back in April.
Sadio Mané begins his suspension while Nathaniel Clyne (muscular) and Adam Lallana (thigh) remain sidelined with long-term injuries.
"It's our fault", said Klopp. Oh my, Liverpool are denied by the woodwork! With two goals and two assists from the first four league matches, he has slotted straight into the team and continued the form he showed in Italy last season. There were times when he tried to play through balls into a closed gap, or looked to shoot when a pass would have been more appropriate.
"A lot of parts of the game I was really happy with".
It's 7th v 8th in this Saturday kick-off as Liverpool and Burnley hope to gain ground on their rivals early in the season.
Klopp addressed the situation after the game and it appeared to be a "better safe than sorry" scenario.