Rodgers watched his side secure a goalless draw on his return to former club Swansea yesterday, where they lacked the cutting edge to claim the three points despite having several presentable chances.
Jose Enrique had a goal ruled out on a marginal offside decision, which Rodgers disagreed with, while Raheem Sterling struck the bar and Luis Suarez twice tested Gerhard Tremmel in the Swansea goal.
The result leaves Liverpool 11th in the Premier League, a point and two places below the Swans, but their performance suggested progress is being made in the adaptation to their manager's passing principles.
The Reds are only five points adrift of Merseyside rivals Everton in fifth, but Rodgers does not expect January to help bring about a huge leap up the table and admits he does not yet consider the current squad to be his own.
He said: "It will evolve. The guys are working very well, they have been fantastic, but we all know you need to get in your own types of players before you can say it is your own side.
"When I came to Swansea in my first season there were 12 players that were used and six moved on. In the second year seven came in over the course of the season and there were nine who went the other way.
"Until you get that turnover of players you can only look at it then as your team. But we will work with the players we have."
Rodgers does not expect there to be major alterations to his squad in January, given the amount of money spent prior to his arrival.
He said: "I am not so sure it will be in January to be honest.
"This year the club wanted to balance the books and see where it was at.
"There was a big investment in the club and obviously a lot of players went out in the summer and a few came in.
"We will look to do some business in January to help and support the players here, but that is where we are at as a football club and it is something the owners trust me to grow over time. Eventually we will get there."
Swansea manager Michael Laudrup, meanwhile, was happy with a point and pleased to see his side record a first clean sheet since August.
He said: "I don't remember the last time we had a clean sheet. To me if it is 2-2 or 0-0 it the same, but I know for defenders and goalkeepers it is important and it was nice for us.
"To extend our good run is important.
"We have a difficult week with three games in six days and we want to try and extend it further.
"If we win on Wednesday (against West Brom) it will give us 20 points already which would be fantastic after 14 games."