She quit the role accusing the UK party leadership of treating Scotland like a "branch office".
Jack McConnell, who was Labour first minister from 2001 to 2007, said he was "very, very angry".
While his predecessor Henry McLeish said Labour faced a problem of "historic, epic proportions".
Ms Lamont announced her resignation in an interview with the Daily Record.
She said: "Just as the SNP must embrace that devolution is the settled will of the Scottish people, the Labour Party must recognise that the Scottish party has to be autonomous and not just a branch office of a party based in London."
Ms Lamont also attacked those who had attempted to undermine her position as she sought to reform the party in Scotland.
Mr McLeish, a former Westminster MP who returned to Scotland and led Labour at the Scottish Parliament from 2000 to 2001, said: "Labour in Westminster, Labour in London has not a clue about the realities of Scottish politics.
"Joanne has been badly advised. The influences on Ed Miliband have not been helpful."
Mr McLeish said Ms Lamont had been unable to lead the party in Scotland amid "constant sniping" from MPs.
"It's interesting to know that while we've had devolution of government from Westminster over the last 20 years, we've had no devolution of political power from the Labour Party," he added.
Former Scottish Labour leader Jack McConnell tweeted: "This is a truly astonishing development. Johann leaves with head held high. Outrageous treatment of Scottish Labour Party Leader."
Lord McConnell later told BBC Radio Scotland's Good Morning Scotland programme he was "very angry".
He said Ms Lamont, who was given more power than previous Scottish Labour leaders when she was elected three years ago, must share some of the blame for failing to set out "a positive vision for the 21st century".
Lord McConnell added: "But to undermine her position in this way, when the position of the Scottish Labour Party leader was clarified so clearly three years ago, is in my view entirely the wrong way to go.
"I think there are serious questions that need to be asked about what has happened in these past two weeks, but also that this issue has to be resolved in advance of the election of the next leader of the Scottish Labour Party."
Lord McConnell said Ms Lamont's move to publicly blame Mr Miliband and "those around him" was a "very serious accusation" that required answers from him and those closest to him.
Two former first ministers of Scotland have hit out at Labour's treatment of Johann Lamont who has resigned from the post of Scottish party leader.