The Reds have picked up just 16 points from 14 games, winning only three, and languish in 12th place in the Premier League table ahead of Saturday's match at home to Southampton.
"It is realistic, absolutely," Rodgers told reporters. "Teams are taking points off each other. Let's be honest, it is a big ask, a massive ask, but that has to be our target.
"We are going to look to try and get as close to that as we possibly can."
Liverpool, who last won the English title in 1990, are closer to the drop zone than fourth place and a shot at qualifying for the Champions League, Europe's elite club competition.
Rodgers, badly in need of adding firepower in attack to support Luis Suarez in January, did his best to put a positive spin on a hugely frustrating start to the season.
"The table is very tight and we have had a run of games where we didn't quite have the wins we wanted but we played well," said the Northern Irishman.
"Now we have to show the winning mentality," added the former Swansea boss, looking for an instant response after his side's defeat at Spurs in midweek.
"Over the course of the next month there is an opportunity to gets wins on the board. I am only looking upwards.
"I have an inherent belief in the group and that will continue to grow. If I didn't have that, I would be concerned."
The return from injury of Brazilian midfielder Lucas Leiva provides a welcome boost for a Liverpool side which also looks light in midfield.
"[The players] are not strolling about. They are giving their maximum. We went into the changing room after Wednesday's game and wondered how we lost it," said Rodgers.
"My job is to keep that confidence, belief in the group because eventually it will change, whether it is through one or two additions or whether we find some form and get some goals.
"There's no doubt we need to get results, I know that as well as anyone. I have got a vision of where I want us to go and I believe we are on track."
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