Carragher told Sky Sports News: "The bigger picture at United is that they're the biggest spenders in Europe and they didn't buy a defender.
"They weren't shocked that Ferdinand was going but they let him go, Vidic announced [he was leaving] in January.
"They're the biggest spenders – how have they not addressed that? To spend that much money and not bring in a top class defender - that's mismanagement."
United go to West Ham United on Saturday in their next league game.