The Reds fear that Steven Gerrard could be out until after the New Year with a hamstring problem, while there are major doubts over Jordan Henderson's fitness ahead of their trip to Tottenham Hotspur this weekend.
The former Sunderland star was seen at Liverpool's Melwood training ground on Monday wearing a foot brace, following an injury inflicted by a challenge from Kevin Nolan which earned the West Ham United skipper a red card in the Anfield club's 4-1 win on Saturday.
Both Gerrard and Henderson have started every one of the Merseyside outfit's 15 Premier League games this season, but Rodgers has insisted that Allen and Lucas can fill the void left by them in upcoming matches against Spurs, Chelsea and Manchester City.
Rodgers told reporters: "Steven is such an important player for us, but we have other players and dynamics in the team and they have to step up. Lucas has been excellent for us and he has forced his way into the Brazil side, so he has that quality and experience to step up and take the responsibility.
"Joe looks like he did when he first came here with his movement, his body work and fluency on the ball and that's what we need right now. We have a number of small players on the field but if we have the ball and the other team hasn't, I think they struggle with it.
"We need that mobility and constant movement in the midfield to get on the ball and knit the game together."
Lucas has made 11 top-flight starts for the Reds this term, while Allen has featured from the off in three of Liverpool's last four games, having previously only been used as a substitute in the Premier League.