Sunday's 1-0 win over old rivals Manchester United at Anfield means the Merseyside giants are top of the table heading into the first international break of the season.
"We have got 35 matches to go," said Rodgers.
"We won't be getting carried away. The team has a lot of improvement to do and there is a lot of work ahead of us.
"The initial challenge is to get in the top four."
They will certainly be pushing for that, particularly if Sturridge maintains his present form.
The former Chelsea man took his overall tally for the season to five and became a match-winner for the third successive game when he turned home Daniel Agger's knock-down in the fourth minute.
Not bad for someone short of full fitness.
"I am delighted with his application because he was nowhere near fit," said Rodgers.
"He played the full game and extra time in the week and he had a slight knock on his thigh.
"But even at 70 per cent he will be as good if not better than most Premier League strikers.
"He had that will and desire to put yourself out there. And once out on the pitch he will always be a threat."
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- Daniel Sturridge
- Manchester United
- Bill Shankly