The Wales international impressed at Anfield after joining from Swansea City for £15m, but his form soon suffered due to a shoulder injury that required surgery.
"The first three months of last season Joe was our best player by a mile but he had a problem with his shoulder which curtailed his season," Rodgers told reporters after the game.
"It meant he could not have that aggressive streak which is part of his game. Joe has been terrific over the course of pre-season and he did very well.
"It is important we have a real strong competitive group as we are trying to build the depth of the group so that I can change the team in games and when we go to play against certain teams I can change the team about."
Allen made 37 appearances in all competitions for Liverpool last season, scoring two goals in the process.