Gerrard faces a spell on the sidelines and is expected to miss the busy festive period after suffering a hamstring injury in last weekend's win over West Ham.
Jordan Henderson is also an injury concern for Rodgers after picking up an ankle injury against West Ham, leaving the Liverpool manager short of options in midfield.
However, Rodgers is confident Allen, who has recently returned to the fold after injury and a loss of form, and Lucas will be able to cope with the demands of five games in 15 days over December.
"Steven is such an important player for us, but we have other players and dynamics in the team and they have to step up," said Rodgers.
"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."