The now West Brom boss is preparing to be reunited with the Anfield club on Saturday - two months after being sacked and replaced by Kenny Dalglish.
Hodgson's brief spell in charge of Liverpool was accompanied by the fans calling for Dalglish to take charge, and he says he knew that his time was up once former owners Tom Hicks and George Gillett left the club.
He told the Daily Mirror: "The people who employed me didn't stay too long. I think for the new owners they obviously found themselves in a difficult situation because we weren't winning enough games.
"The fans were making it clear they wanted me gone and someone else in. Everyone knows for one minute I can't suggest I felt wanted at Liverpool.
"It is not exactly a secret I wasn't perceived by a lot of people as the manager they wanted at Liverpool. They wanted somebody else and that makes life a lot more difficult.
"It was my misfortune to be at a club where the fans made it pretty clear early on they really wanted the manager they have got now."