Rodgers' side, beaten 1-0 by Basel in the Champions League in midweek, secured a first win in four Premier League games with a tense victory at Anfield on Saturday.
It was enough to move the Reds, who finished second in the Premier League last season, into the top half of the table, with 10 points from their seven matches, but the Liverpool manager knows his team remain short of peak form.
Rodgers made a host of signings over the close-season in an attempt to replace star striker Luis Suarez, who joined Barcelona, and bolster his squad for a sustained challenge in the Premier League and Champions League.
"Performance wise we've still got a way to go," he said. "The speed and movement of our game, the intensity is still developing.
"But I'd rather have that now and do what we've done in the last two seasons and get better and better as the season goes on. While you're searching for that it's important you find a way to win.
"The players have got remarkable character, there are a lot of young players here and new players coming finding out what it's like to be at a big club.
"A full squad to pick from gives me the chance to look at different ideas if I need to and hopefully we can go on a run.
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