Saturday's thumping 5-1 victory over Arsenal closed the gap to the side at the top of the table, which is now Chelsea, to six points but the Reds boss refuses publicly to consider a charge for the championship.
That does not, however, mean he is not looking at ending Liverpool's barren run without a title stretching back to 1990 sooner rather than later.
"I came here to challenge for titles, so there is no limit on our ambitions," he said.
"I came to this great club hopefully to be here for a number of years in order to bring back the success and continue on from some of the great work the likes of Kenny (Dalglish) was doing here before I arrived.
"The momentum has been building and building but I just think it's unprecedented to go from being where we were last year in seventh position (to first).
"I am very much full of optimism for this football club and the development of the team but I also have to be realistic as well and I think it's something that might be too much for us this season.
"But that doesn't stop us fighting or wanting to be the best we can be, and at some point in my time here we will be ready.
"Make no mistake, I want to get into the Champions League for the people here at the club and the people of the city.
"I came here to try to inspire the city as much as the team. I know what Champions League football can bring to a city like Liverpool and everything it can generate.
"I keep the focus on improving the players, improving our performance levels, and you can see from the continuation of the development we've made over the last 18 months that we're going to be a match (for other teams in the title race).
"I won't talk about horses and all sorts of things (in reference to Chelsea boss Jose Mourinho's metaphor after beating Manchester City last week), we'll just talk about football and making people better."
Liverpool have been undone slightly this season by the odd slip in consistency, often after a big performance against one of their top-four rivals, and results in the last couple of months have highlighted that.
They were excellent at Manchester City on Boxing Day but came out 2-1 losers and failed to raise their game for the trip to Chelsea immediately afterwards.
Everton were dispatched 4-0 in a midweek Merseyside derby only for a 1-1 draw to follow against struggling West Brom but Rodgers insists the pressure of expectation is not a problem.
"If you are talking about can they cope with pressure then you look at the last few games we've had - Tottenham away (a 5-0 win), Everton at home, the game on Saturday.
"That (pressure) can only hurt you if you let it. If you read into things like that too much and listen to too many outside influences or the background noise that goes on then it can hurt you.
"I have never been one who has let anything like that affect what I have done in my life and that is the message I will put across to the players.
"My job is to release the pressure from them so they can play and organise their work."
The average age of the squad is around 26 and it remains to be seen whether that youthful outlook will be a boon or a burden in the remaining 13 matches of the season.
Rodgers believes he has seen enough character in his younger players to suggest that will not be a problem.
"We have Raheem Sterling at 19, Jon Flanagan at 20, Jordan Henderson at 23 and Philippe Coutinho at 21 - it is not affecting them because they are concentrating on their performance," he said.
"I have a great belief in the players I have here and we want to build on that but I take great pride in making people better on the field and helping them off it.
"I look at Jon Flanagan and his development as a young player since I have been here.
"He is an absolutely outstanding character and he has gone into the big pressure games and been outstanding.
"Many of our other young players - Jordon Ibe is 18 and came off the bench against Arsenal - have been excellent."