Early fixtures against the likes of Arsenal, Manchester City and Manchester United contributed to the Reds' worst opening to a league campaign for more than a century.
It has taken a while to claw their way back but they head into this weekend's fixtures only four points adrift of fourth place.
Last Sunday's win at West Ham was the first time in almost a year Liverpool had won back-to-back league matches and having progressed to the last 32 in the Europa League, Rodgers senses something of a turnaround.
"You're always striving to have more and be better but as I sit here today, having experienced the last six months, I'm quietly pleased with how it's evolving," said the Northern Irishman, who took over from Kenny Dalglish in June.
"We're a long way off where I want us to be, of course, but we've shown we're making good progress.
"By all accounts Liverpool have had a disastrous start but we're four points off the top four and if we had a little bit more luck, we actually could be in there now.
"The great encouragement is we're only going to get better.
"I hope that we finish this year strongly. 2012 has been an emotional year for the football club, we want to finish it on a high.
"We can then go into the next six months and push on, because that's when you take care of business and in particular the last 10 games.
"If we can arrive in January in and around that top four then we can really put our foot to the floor, when the confidence will be improved even more and players will be aligned with what we're trying to achieve.
"I believe we can have a good second half of the season."
There was some more good news for the club after goalkeeper Brad Jones signed a new contract, joining the likes of Luis Suarez, Martin Skrtel, Daniel Agger and Jonjo Shelvey who have all extended their deals since Rodgers' arrival in the summer.
The Australia international believes he has proved himself to Rodgers after the manager initially cast doubts over his long-term future at the club.
"When he came in I don't think he was too sure about whether I was going to stay or not and I had to prove to him I was worthy of being here," Jones told liverpoolfc.com.
"He was very honest with me at the start and said maybe things weren't going to work out.
"But he was then just as honest to come and say to me I'd done well and proved myself to him.
"That's what you want from your manager - somebody that's honest, that you can talk to and is going to help you progress as a player.
"He's a big influence. He's a very positive guy and somebody that wants to be amongst the players, talking to them and making sure they know what he wants.
"I'm happy to stay on and happy the club have been supportive with me and seen enough to want to keep me here longer."
Jones has made 10 appearances so far this season, by far his best run in the side having amassed a total of just 14 since joining from Middlesbrough in 2010.
Despite his up and downs at Anfield he hopes to be part of a successful side over the coming years.
"Obviously there was a difficult time in the middle of that and three managers in that space of time is difficult because football is very much about opinions," he added.
"Some people rate you more than others and I think I've found that in my time here at Liverpool - some managers have thought more of me than others.
"I said when I signed here it was a dream come true. It was something I'd wanted as a young boy - and that hasn't changed.
"I want to stay here as long as I can. At the minute, the club is on a progression and we're improving a lot.
"It's a good time to be here and I'm sure in the next couple of years I'll be part of a successful squad."
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