Rodgers acknowledged the centre-back's commitment to the Liverpool cause will be hard to replace when he retires at the end of the season.
"Jamie Carragher was immense, he's a real colossal player and he's only got two games left for the club," the boss told his post-match press conference.
"His influence is superb, on the training field every day and in the changing room. He's so professional.
"You saw him out there at 35 and he was at the top of his game.
"He was absolutely outstanding - and having worked with him for so long, I can clearly see why he was one of Europe's top defenders for so many years.
"We'll have to search far and wide to get someone in to be at that level."