Hodgson faces his old club tomorrow at the Hawthorns.
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."