The Reds are currently third in the Premier League, two points behind leaders Arsenal.
However, the Northern Irishman has poured cold water on suggestions that his side can mount a sustained push to win the league this campaign.
"We're here to compete; Liverpool is one of the great institutions of the game. We're never happy when we don't win, but you have to have a sense of perspective as well," Rodgers told the club's official website.
"There will come a time when we start looking at when we can challenge, but we can't get carried away. The club finished eighth the year before I came in, and we finished seventh last year.
"We have stabilised the mentality, there's a strong culture at the club now, and I think the supporters can see the direction we're going in. I still think there's a hell of a lot of improvement for us to make, but in the main we're a tight unit, and we just need to keep moving forward."
Rodgers's side are unbeaten in their last three games and drew 2-2 with Newcastle United on Saturday.