The Scot left the club on Wednesday following a mixed 17 months in charge at Anfield in which his side enjoyed League Cup success and reached the FA Cup final but suffered from poor form in the Premier League.
Dalglish tweeted: "Overwhelmed by support of the fans. Always been special but even more so now. Thank you from the bottom of my heart. YNWA and I never have."
|Liverpool react to boss' removal
His removal marked the end of his second spell in charge of the club, after he previously oversaw a six-year trophy-laden stint which ended in 1991.
The Scot is still revered as one of the Reds' greatest-ever players and is widely respected for the role he played following the 1989 Hillsborough disaster.
Liverpool's American owners, Boston-based sports consortium FSG, are believed to be currently targeting Wigan boss Roberto Martinez to replace Dalglish, as Goal.com exclusively revealed on Thursday.