Victory over Sunderland at Anfield on Wednesday night would leave Liverpool one point behind leaders Chelsea with seven games left.
And while manager Rodgers continues to straight-bat all talk of a possible first title since 1990, the reality is that his free-scoring team have become major silverware contenders.
Luis Suarez's sixth Liverpool hat-trick in a 6-3 win at Cardiff saw him equal Robbie Fowler's club record tally of 28 Premier League goals in a season, while a Martin Skrtel double and Daniel Sturridge's late finish floored the relegation-threatened Welsh side.
"We are focusing on the immediate future," Rodgers said.
"The fans can believe and dream, and when you come to see your team play away from home and they score six goals, you've got every right to do that. They have been a big part of our success this year.
"I've got to say that I am really looking forward to the Sunderland game. It feels like we haven't played at home for ages.
"Wednesday will be a great night for us. We've now got five games left at Anfield, with three away from home. Anfield is a special place to play football, so for us, it's about the immediate future."
Liverpool did not have things all their own way at Cardiff City Stadium as the they twice trailed to goals by Jordan Mutch and Fraizer Campbell, but there was no stopping them once Suarez, Sturridge and company started wreaking havoc.
"We don't work to just outscore teams; we work on our balance," Rodgers added. "We are certainly not a team that is not worried about defending, that's not the case at all.
"We were off the back of two clean sheets - which I take as much pride in - against two difficult teams, Southampton and Manchester United.
"We conceded too much space, but the key thing is how we respond and how we have grown over the last 18 months. There has been that resilience and confidence to know that we can get back in the game.
"We will analyse the other elements of the game that we can be better at. That will always be the case - you'll always look to improve.
"Look at our imagination and creativity. You sensed the crowd felt that every time we were in their half, we could score. That is a wonderful recognition of the type of team that we are."
Rodgers also paid tribute to Skrtel, who scored the second and third goals either side of half-time before Suarez inevitably hogged the headlines.
"Every team needs goals from everywhere on the pitch," he said. "That was one of the things I said at the beginning of the season. The defenders have to chip in.
"That's the sixth goal he (Skrtel) has scored this season. He is great at attacking the ball - he finishes like a striker. He has been a real stalwart for us this season."
Cardiff remain firmly in the relegation zone following their latest loss, and attention now switches to a key encounter at fellow strugglers West Brom next weekend.
"We will keep fighting," City manager Ole Gunnar Solskjaer said.
"We were fantastic in the first-half. When you play against an attacking side such as them you have to test their back-line, and I think that is what we did.
"We had spaces in a few places and got some fantastic goals. Liverpool didn't come up with much in the first-half, chances-wise.
"We faced the top scorers in Europe, with the teams around us looking like having more manageable games (on Saturday), and we are not worse off than we were at the start of the day. I think that is the biggest plus that has come out of it."