Manager Jurgen Klopp said he still has "a lot of work to do" after Liverpool's hard-fought 1-0 victory over Brighton sent them top of the Premier League.
Mohamed Salah, who scored 32 league goals last season, scored with a clinical strike midway through the first half at Anfield.
"Nobody doubts we deserved the three points and that's the important thing," said Klopp.
Liverpool, the only Premier League side with a 100% record after three games, are two points clear of champions Manchester City, who drew 1-1 with Wolves earlier on Saturday.
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