Liverpool pushed on from their strong end to the first half and should have been in front within seconds of the restart, only for Sturridge to slot the ball wide of an empty net once played clean through by a poor Christensen back-pass.
Liverpool, though, will quickly have a chance for revenge as they head to Chelsea protecting a flawless Premier League record for a blockbuster Stamford Bridge clash on Sunday (AEST).
Eden Hazard struck an early psychological blow for Chelsea ahead of Saturday's Premier League clash with Liverpool by ending Jurgen Klopp's 100 percent start to the season with a wonder goal to seal Carabao Cup victory at Anfield.
Stunner: Chelsea's Eden Hazard (centre) celebrates with teammates after scoring the winning goal at Anfield.
Emerson Palmieri nudged home the equaliser before a phenomenal solo goal from Hazard booked Chelsea's passage into the last 16. Ross Barkley's header was pushed away by Mignolet but Emerson was the quickest to react and poked the ball across the line. The linesman is in a really good position.
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Chelsea will face Liverpool once again on Saturday in the Premier League but Zola does not think Wednesday's result will influence the outcome at the weekend.
VAR was used to check whether Barkley was offside but the decision was not reversed. Fabinho is being gradually introduced into first-team duty, while fellow new signings Keita and Xherdan Shaqiri were also given starts.
Keita, who was the brightest of Liverpool's forwards in the first half, drew a brilliant save from Caballero as he cut inside onto his right, as the game came closer to an opener.
"Eden's growing fast, he's growing fast in maturity, in choices he's making on the pitch and I think, in my opinion, we haven't seen the best yet".