Liverpool held a long interest in Southampton defender Virgil van Dijk but the Saints refused to do business and were able to keep hold of the Dutch defender.
Andy Robertson was the only defensive player to join Liverpool in the summer as Jurgen Klopp opted to strengthen his attacking options with Mohamed Salah and Alex Oxlade-Chamberlain.
And critics are now questioning Klopp and Liverpool’s transfer policy following their struggles in defence this season.
Liverpool have kept just two clean sheets so far and next face Manchester United, who have been miserly in defence with just two conceded all season.
Last term, United struggled for goals but they addressed their problem by signing Romelu Lukaku.
And Carragher believes Liverpool’s mistakes in the window demonstrate the difference between them and United.
Carragher told The Telegraph: “This is a fundamental difference between the modern Liverpool and United: one club recognised its weakness and fixed it, and the other is beset by the same problems.
“United did not score enough goals so spent £75 million on Romelu Lukaku. He was not United’s first choice.
“They were pursing Antoine Griezmann and Alvaro Morato, but when those deals fell through Mourinho did not hang around. He did not wait a year for Griezmann. He wants the title now.
“Liverpool conceded too many goals so wanted Virgil Van Dijk. They put themselves into a position where he was ready to join but messed up. Instead of lining up alternatives they spent the summer hoping Southampton would change their mind.
“It was Van Dijk or no one, which led to the season starting with Liverpool continuing to concede soft goals, failing to win games they dominate, dropping points to teams in the bottom half.
“Liverpool cannot afford these mistakes on and off the pitch – not only to challenge for the Premier League but to remain in the top four.”