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.
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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.
Klopp added: "[Manchester City boss] Pep Guardiola said this week the players are still not 100% fit and that's how it is.
"You cannot given them no summer break, a very short pre-season and then say be at your best. These games are the best sessions we have to get fit.
"I knew before the game I had a lot of work to do and maybe now you know it as well."
Liverpool were not at their fluid best, with their most dangerous moments coming before Salah struck.
After Sadio Mane poked a shot just wide, Roberto Firmino drew a smart save out of Mat Ryan with a downward header before Trent Alexander-Arnold hit the bar with a free-kick.
Brighton claimed a stunning 3-2 win against Manchester United in their previous game but rarely threatened to follow that up with an upset at Anfield.
They did, however, give the hosts some nervous moments in the closing stages and were denied a point when Alisson saved superbly from Pascal Gross' header.
"I'm really not interested in the table. It's really not important after the third matchday. Nine points are important," said Klopp.
"I expect a lot from the boys. I'm pretty demanding but I know we can improve."