Sturridge nearly restored Liverpool's lead after hitting the bar but it was Chelsea who snatched the victory as substitute Eden Hazard came off the bench to score a superb solo goal to make it 2-1 in the 85th minute.
They then travel to Stamford Bridge at the weekend aiming to preserve their 100 per cent start to the 2018-19 campaign.
The away side levelled when Hazard, introduced two minutes before Sturridge's goal, delivered a free-kick into the Liverpool box, Barkley's header was palmed away by Mignolet and Emerson prodded in. These players are able to play this game, Jorginho in midfield is a big influence.
Sturridge should have put Liverpool ahead immediately after the restart, but, having intercepted a awful Gary Cahill backpass and rounded Caballero, he shot wide of the open goal.
However, it's been six long seasons since the Anfield giants last won a trophy and the Carabao does present, arguably, the best chance of getting silverware this season. Every player was a full worldwide, with the likes of Cesc Fabregas, Emerson and Ross Barkley handed opportunities to stake a claim for more Premier League action.
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He played the full 90 minutes as the Red Devils were held to a frustrating 1-1 draw by Wolves in front of their home fans in the Premier League on Saturday afternoon.
Virgil van Dijk paid lip service to the idea of full commitment by insisting Liverpool wanted to win every competition. "That is a really good group, a really strong football team".
A lot of eyebrows were raised and understandably so when Liverpool paid Southampton £75 million in January to make the towering Dutchman the most expensive defender in the history of world football.
- Sturridge has netted 11 goals in his last 11 League Cup appearances.
Manchester City, the current champions, remain the favourites to win the league ahead of Liverpool, but Klopp believes Chelsea have the strength and the title-winning experience to make them contenders.