They next face Arsenal - who thumped Nottingham Forest 5-0 - at home in the fourth round.
However, there's a real chance that the Reds could be kicked out of the competition after the EFL launched an investigation.
According to The Athletic's James Pearce, formerly of the Liverpool Echo, one of Liverpool's players "may not have satisfied the registration criteria to feature in the competition".
The potentially ineligible player hasn't been named, but if Liverpool are found guilty, it's within the EFL's power to fine or even throw them out of the Carabao Cup.
"The club are aware of a potential administrative issue pertaining to one of our players," a Liverpool spokesman said.
We are working with the relevant authorities in order to establish the facts of the matter and will be making no further comment until this process is complete.
Arsenal fans will be praying Liverpool are found guilty, though the Anfield side can argue that Sunderland were only fined for fielding an ineligible player - Ji Dong-Won - in 2014.
Jurgen Klopp made 11 changes to his starting XI to face MK Dons, with 16-year-old Harvey Elliot, 18-year-old Curtis Jones and 20-year-old goalkeeper Caoimhin Kelleher handed full debuts.
Rhian Brewster also started upfront, while 22-year-old Pedro Chirivella made a rare appearance off the bench having not played for the first team in over three years.
Who the ineligible player was remains to be seen, with an EFL spokesman saying: "We are currently considering the matter."
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