Kerry McCarthy said MPs appointed by Mr Corbyn would have to “go through the pretence” of saying they believe he would make a good prime minister.
She claimed she did not see how this “hurdle” would be cleared by elections to appoint shadow cabinet members.
Ms McCarthy was among the first batch of Labour MPs who quit Mr Corbyn’s shadow cabinet in an attempt to oust him from power by claiming they had no confidence in his ability to win a general election.
She told Pienaar’s Politics on BBC Radio 5 Live that there were things in her role as shadow environment secretary she had been “reluctant to walk away from”.
Ms McCarthy went on: “The question would be though is I felt I couldn’t go on the media and say that I had confidence in Jeremy Corbyn.
“I think if you’re in the shadow cabinet in particular you’re going to get asked that question and you’ve either got to be able to go through that pretence of saying ‘Yes I think he can be prime minister, he’ll be a good prime minister’ or not.
“And I just don’t see how with shadow cabinet elections... how you get over that hurdle.”
Ms McCarthy also said there are “certain echoes in politics today” of her political experiences from 1983 when she met “sort of very middle class students who basically cheered every time the unemployment figures went up”.
She noted these University of Liverpool students believed at the time that increases in unemployment would “bring the revolution a day closer”.