The Anfield outfit stumbled out of the blocks, with a testing fixture list leading to them making their worst opening to a campaign in more than a century.
Rodgers would have been hoping to avoid a baptism of fire after inheriting the managerial reins from Kenny Dalglish over the summer, but he has seen his patience rewarded over recent weeks.
Liverpool are back into the top-half of the Premier League table, through to the last 32 of the Europa League and looking to carry the momentum they have established into what they hope will be a productive 2013.
"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 Rodgers.
"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."
He added: "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."
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