The 72-year old has enjoyed a long, respectable managerial career in the game but his stint at Anfield was a monumental disappointment and he lasted less than a season on Merseyside - leaving by mutual consent with the club four points off the relegation zone.
There were plenty of questionable decisions made by Hodgson as Liverpool boss, but getting rid of the wrong player really does take the cake.
The story goes that Hodgson drafted in Paul Konchesky, who he'd worked with at Fulham, in the summer transfer window. The deal saw Liverpool youngsters Lauri Dalla Vale and Alexander Kacaniklic head in the opposite direction.
But it later transpired, courtesy of Kacaniklic, that Hodgson had actually offloaded the wrong 'Alex' and by the time he realised, it was too late to halt the move.
"It was a bit difficult for Liverpool to replace me," the Swede said, as per Liverpool Echo.
"In his head, he thought he had changed another Alex for Konchesky. But then it was too late. It's a little funny.
"Then he just told me I was welcome back in Liverpool with open arms, but that I should do what I felt. Then I had already changed my mind and was very excited about coming to Fulham."
Having failed to make an appearance for Liverpool's first-team, Kacaniklic went on to play 100 times for Fulham and later turned out for French side Nantes in Ligue One.
The deal by Roy Hodgson at LFC to give Fulham £3m + Lauri Dalla Valle & Alex Kacaniklic for Paul Konchesky is still astoundingly awful.- Jack Bezants (@JBezants) November 10, 2012
He now plays in his native Sweden with Hammarby, where he's been for the last two seasons. On the international stage, Kacaniklic has made 21 appearances for his country, scoring three goals.
Had Hodgson sold the right player, who knows how his career would've panned out.