After three wins and a draw from their opening four matches of the season, Liverpool were the early pace-setters in the league, however defeat to Southampton saw them relinquish top spot.
Another defeat to Manchester United in the League Cup on Wednesday means Rodgers' side only have the league to focus on until they enter FA Cup in the new year, and the 46-year-old wants his side to use that to their advantage.
"Now we can only concentrate on the league up until Christmas," he 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, however 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 stabilise his life," Rodgers added.
"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 distraction and we can get to the level of performance of the first four or five months of last season."
