The win moved Liverpool into the top half of the Premier League and a run of form that has seen the Anfield club lose just once in the league since September 23 means they are just four points off the top four.
Rodgers, 39, is keen for his players to continue to develop their understanding of the style of football he has been implementing since taking charge of the club in June, rather than setting end-of-season goals.
When asked if the top four was now a realistic target Rodgers said: "We are just trying to build our momentum.
"We had a difficult opening fixture list and coupling that with trying to play a certain way of football was always going to be difficult.
"Certainly over the past couple of months we have been progressing and just let's see where we finish.
"This is one of the biggest clubs in world football and everybody knows where it should be but we are making steady progress and climbing the league and it is important for us to do that."
Sam Allardyce saw his West Ham side hit back after falling behind to Glen Johnson's opening goal for the visitors to lead at half time through a Mark Noble penalty and a Steven Gerrard own goal. But a second-half goal from Joe Cole and an unfortunate James Collins own goal meant the Hammers were still searching for back-to-back league wins this season.
Allardyce's side are in the midst of a tough run of games and the former Blackburn manager is pleased with how his relatively small squad have coped.
He said: "We have...managed to get some points off Chelsea, Newcastle away and we drew here with Man City.
"We haven't done too bad. (We drew) with Stoke, played well and might have won that one, so we haven't done too bad in this period with the size of teams we have played."
Of more concern to Allardyce is the growing injury list with Mohamed Diame's apparent hamstring tear in the 73rd minute yesterday adding to the problem.
West Ham are already without a host of first-team players, including the likes of Andy Carroll and Yossi Benayoun, and Allardyce knows how important it is to get them back as soon as possible.
"The biggest and most disappointing thing is the injuries we have collected during this period," he said.
"Trying to get the other players back as quick as we can is going to be really what the medical staff must really focus on."