Liverpool appear to have finished on the superior side of the €160m deal.
But Carragher told the Telegraph: "I can't understand Liverpool's decision to sell Coutinho now. Not mid-season.
"No matter how much I hear about boyhood dreams; efforts to convince him to stay and how much family, representatives or even sponsors pushed for it, why this month?
"They have a kind Champions League draw. The Liverpool team of January 2018 is superior to that of January 2005, which won the competition. They have lost just four of their last 44 games, continuously improving. Why endanger momentum?"
But he also added: "Having been criticised a few year ago, Liverpool's recruitment team has been more astute recently; Mo Salah, Sadio Mane, Roberto Firmino and Joe Gomez have proved to be exceptional signings.
"These recruits ensure Klopp can direct his resources on pursuing one or two high class players rather than six or seven, as was the case with the Suarez money."