Liverpool scraped past Middlesbrough in the third round last night, in what was a thrilling match at Anfield.
The game finished 2-2 after extra-time, before Liverpool eventually won the penalty shootout 14-13.
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Arsenal's indifferent start to the season continued, after they were beaten 2-1 at home by Southampton.
Everton crashed out 3-0 at Swansea, while last season's runners-up Sunderland went down 2-1 to Stoke.
Elsewhere, there were wins for Bournemouth, Derby, Sheffield United, MK Dons, Shrewsbury and Fulham.