Dalglish felt he still had plenty of work to do and despite many fans' unhappiness at the removal of the club's iconic figure, the 61-year-old urged supporters to get behind principal owner John Henry and chairman Tom Werner.
"I would hope nobody would prejudge things now," he told the Liverpool Echo.
"The owners have their own reasons for doing what they have done. They came in to help the club at a time when it wasn't in a great condition.
"They have improved it, taken it forward and are doing the best they can.
"Liverpool is still a great football club, still a club that should believe in whoever is going to come in after myself.
"The supporters, not just for myself but for everyone else, have always been fantastically supportive of the team and that should not change."