The Reds boss has targeted a solid run until January, when he can further reinforce his squad, while also urging Raheem Sterling to concentrate all his efforts on his career.
After three wins and a draw from the opening four matches of the season, Liverpool was the early pace-setter in the league, though defeat to Southampton saw the Reds relinquish the top spot.
Another defeat to Manchester United in the League Cup on Wednesday means Rodgers' side only has the league to focus on until it enters the FA Cup in the new year, and the manager wants his side to use that to its advantage.
"Now we can only concentrate on the league up until Christmas," Rodgers said. "So we have to make sure we stay up in that top six in the league and keep fighting, and hopefully we can reinforce in January.
"I think the players have made an excellent start. We were flat and subdued at the weekend [against Southampton] and we couldn't get going - part of that was because of the players we had available."
Rodgers has also challenged Raheem Sterling to focus on improving his performances on the pitch after more problems off it. The winger was arrested for alleged assault earlier this year, although the case against him was dropped and he was officially cleared.
"Raheem needs to have a clear mind in everything in his life - he needs to stabilize his life," Rodgers said. "We mustn’t forget he is 18 - but he has to understand the remarkable opportunity he has at one of the biggest clubs in the world and focus everything in on his career.
"Once he does that and he is clear in his mind, he has no distractions and we can get to the level of performance of the first four or five months of last season."