Liverpool have been very inconsistent in the Premier League this season with their last two matches - woeful in defeat to Stoke, excellent in beating QPR - encapsulating their form.
Many have been quick to point out there does not appear to have been much progress made since last term.
But Rodgers - who will be back in the dugout against Sunderland on Wednesday after missing the QPR trip with illness - is confident there is time yet to improve things.
"This is a period of time where you have to keep your head down and work hard and give the players every chance to perform," he said.
"The second half of the season, and in particular the last 10 games, I believe you are working to because that is the business end when things are decided.
"When you arrive at that period you want to get yourself in a good position to challenge, whether that is in the league or cup competitions.
"We can still achieve our objectives this season so when you can do that going into the second part of the season it gives you real hope."
Liverpool have been waiting to finalise a deal for Chelsea striker Daniel Sturridge but that will not officially be completed before the visit of Sunderland.
Blackpool winger Tom Ince has also been linked with a return to the club he left in the summer of 2011 but those negotiations are proving more difficult.
Aside from that Rodgers is not planning a huge amount of business as he knows there is not a lot of money to go around.
Rodgers admits it is always difficult trying to secure significant signings in January but he is happy with the backing he is getting from owners Fenway Sports Group.
"Even if managers have a player they think they might lose they don't want to lose him in January, they at least want to get him through to the end of the season," he said.
"The support the club will give us will be excellent. The owners have been great and I have no complaints in terms of where we are as a club at this time."
Rodgers has now completed seven months at the club, having succeeded Kop icon Kenny Dalglish who was sacked in May.
Despite results not being quite what he would have wanted he is enjoying the experience as boss of one of the most high-profile clubs in the world.
"You are very much in the public eye far greater - that is the single biggest thing," said the former Swansea manager.
"But I love the expectancy and challenge of making this great club great again.
"That period (since taking over) has been fantastic and I believe as we grow and work more together we will improve."