Liverpool are six points behind current leaders Chelsea and travel to Fulham on Wednesday evening, but expectations have been raised on the back of Saturday's stunning success at Anfield.
However, securing a UEFA Champions League place next season continues to be Rodgers' principal objective.
"I really only focus on the team and the football club, and make no mistake - I want to get into the Champions League for the people here at the club and the people of the city," he said.
"I came here to try and 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.
"The momentum has been building and building, but I just think it would be unprecedented to go from being where we were last year in seventh position to first.
"We've got so many young players, who are still growing and developing and our squad is small. So I feel that we've still got work to do.
"But when we play like that and perform like that (on Saturday), people are obviously going to ask the question (can you win the league?).
"We're five points behind Arsenal, four behind Manchester City and six behind Chelsea and we still have them to play here at Anfield.
"But the main objective is just to finish as high as we possibly can and let's see where that takes us.
"Right the way through this season and throughout my time here, we've started to just chip away in our development and improve.
"It was another wonderful result for us (on Saturday) and what was particularly pleasing was the performance.
"It was an incredible display from a group of young men who are growing and getting better all the time. It was very pleasing."