The Reds boss says his side harbors hope of catching the Premier League leader after twice coming from behind to beat the Cottagers via an injury-time Steven Gerrard penalty.
The visitors went behind after an own goal from Kolo Toure and Rodgers called for his players to iron out individual mistakes in the remaining matches.
"We conceded two goals, that has been unlike us for a while. We need to eradicate the individual errors. Thankfully we have goals in the team," he told reporters.
Steven Gerrard clinched the three points for the Reds by converting an injury-time penalty and recieved special praise from his manager.
He continued: "Steven Gerrard is peerless in situations like that. He showed brilliant composure. It was a great result. We've had to show character to come form behind twice. A brilliant victory."
When asked about Liverpool's title aspirations, the northern Irishman remained coy and replied playing down his side's chances.
He added: "We're going to keep pushing. We've shown enough times we're a very good side. We're chasing, other teams are still ahead of us. We need some of them to drop points. We know we still have Man City and Chelsea to play at home. We'll take it game by game. I'm enjoying as a coach watching the team improve."
The Reds boss also reserved some praise for Fulham, which was twice ahead in a rollercoaster of a match.
"It's a great credit to Rene and his staff and players that we were given a very tough game. In the first half we were not quite on it in terms of intensity, and a mistake has put us 1-0 down," he said.
"We then got a good goal, thanks to Gerrard's marvellous pass. We raised the intensity and aggression at halftime. We're disappointed with the second goal we gave away. This team has shown great characteristics mentally."