Luis Suarez, Raheem Sterling and Steven Gerrard's late penalty fired the Anfield outfit to a hard-fought 3-0 victory away to Southampton at St Mary's.
With Arsenal going down 1-0 at Stoke and Manchester City distracted by the Capital One Cup final, Liverpool are now the closest challengers to leaders Chelsea, who hold a four-point lead.
With just 10 fixtures of an enthralling title race remaining, Rodgers would not be drawn on how many matches he wants his side to win, but again claimed that they are outsiders in the race.
He told Sky Sports: "We just want to keep winning games. There are 10 games to go now and we'll just see where it takes us.
"We only want to win the next game, that's our next focus. We don't want to get ahead of ourselves.
"We're enjoying our football, we're working very, very hard. Our idea now is to win the next game, and that's our only focus. I think for us we're just keeping going with what we're doing.
"Everyone speaks about Chelsea, Manchester City and Arsenal, and rightly so. They're the three teams that have been up there for a number of years.
"We're only concentrating on ourselves. I take great pride in working with the players and great pride in watching them and how they've developed over the 18 months.
"We just want to keep improving. Mentally, we are getting stronger all the time. Tactically, there is a number of formations that we've played this year.
"Our style will always try to be the same, but it's good to have that flexibility in the team."
Rodgers was delighted with the efforts of his players at Southampton, as they adapted to a new formation and kept a clean sheet after significant focus on their recent defensive deficiencies.
He added: "I thought tactically the players were brilliant. We played a 4-4-2 diamond to try and give us the numbers in the middle of the field.
"Defensively we were outstanding - blocked lines, blocked spaces, we pressed the ball. We got three goals and could have had five or six again.
"I think the performance in terms of defensively is up there with the Arsenal game. This is a really difficult place to come, Southampton are an excellent side and press the ball really well.
"It was an all-round outstanding team performance both with and without the ball."