The Scot left the club after 16 months in the job after the American owners decided an eighth-placed league finish was not sufficient evidence to suggest he could fulfil their vision for the future.
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."
Dalglish was criticised for many of his signings - Stewart Downing, Jordan Henderson and Andy Carroll in particular - but having stabilised the club in the wake of Roy Hodgson's departure he believes he leaves his successor a great foundation on which to build.
"You cannot underestimate the pressure that is on a boy who comes to play for Liverpool," he added.
"But in the first year, what they have done has been a credit.
"There is now a great foundation to build on and to move forward with.
"Taking aside the decision made about myself, for four players to be in Roy Hodgson's England squad for Euro 2012 and for Jordan Henderson to be on standby as well is a great credit to the players.
"It's fantastic for the club and those players - and I hope they go on and represent everybody well."