Hodgson, now manager at West Bromwich Albion, was eventually sacked and replaced by Dalglish after just six months and will face his former club for the first time since leaving on Saturday.
The former Fulham manager said he knew his time was up when unpopular owners George Gillett and Tom Hicks left Liverpool.
Hodgson 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.''