Rodgers's side beat Carroll's West Ham 2-1 on Sunday, and the Northern Irishman, who sold the England international to the Hammers for £15m last summer, praised his former forward.
Rodgers told reporters: "Carroll is one of the best in Europe in the situation where the ball is played up to him. He can be unplayable.
"I thought Martin Skrtel was brilliant in choosing when to drop off and when to intercept [Carroll]."
The Reds host Manchester City on Sunday.