The Match of the Day pundit questioned Allen, claiming that the Wales international lacks impact due to his unwillingness to play the killer pass.
Rodgers has leapt to the defence of his player, and believes that the 22-year-old will justify his decision to sign the former Swansea City man.
"I saw something criticising Joe for not playing risk passes," Rodgers said. "Unbelievable.
"Our so-called pundits who don't know the dynamics of a team and how it functions. Joe will prove an absolute bargain.
"Joe's role is to keep the ball and that in Britain is a special talent. It is such a rare talent for a midfielder to rarely give the ball away."
Allen joined Liverpool from Swansea for £15m in the summer.