Party members who back the embattled UK leader made their feelings known after Ms Dugdale last week joined the calls for Mr Corbyn to step down.
Ms Dugdale insisted Mr Corbyn is no longer “competent” to do the job after a mass of front-bench resignations and overwhelming defeat in a vote of confidence among MPs.
Angela Eagle, tipped as a potential challenger to Mr Corbyn, repeated her calls for him to go, although another rebel Owen Smith backed away from confrontation with the party leader, issuing an appeal to colleagues to heal the rifts.
Ms Dugdale called for politicians to “reach out” to the one million Scots who voted Leave in the EU referendum in yesterday’s speech.
But she heard complaints from activist Les Reid of her own Edinburgh East party branch that Labour MPs had “turned on” Mr Corbyn “for no apparent reason”.
He told the Scottish leader: “Jeremy Corbyn to my mind is the only Labour politician who can appeal to Remain and Leave, he’s the only one who can do that, now he’s being chopped down by a bunch of MPs.”
Mr Reid later voiced disappointment at Ms Dugdale’s position: “I think she should’ve stood by him. There should be solidarity within the Labour Party.”
Ms Dugdale later insisted there is “no split” in Scottish Labour, but maintained her reservations about Mr Corbyn’s ability to lead.
“If he’s lost the faith of 80 per cent of his colleagues, he can’t do his job, he’s therefore not competent to do his job,” she said.