A section of the audience laughed when Owen Smith - who is challenging Mr Corbyn for the Labour leadership - said Ms Dugdale was doing a "brilliant job".
Ms Dugdale, who was not at the debate, has backed Mr Smith's campaign for the leadership.
But Mr Corbyn said he did not think anyone should be jeered.
It comes as allies of Mr Corbyn dismissed claims they could seek to remove Ms Dugdale if Mr Corbyn wins the leadership contest.
Speaking in Edinburgh on Friday, Mr Corbyn said: "I don't think anyone should jeer at anyone else. I don't do that myself and have asked other people not to and made it very, very clear - let's have an honest, open and respectful debate."
Mr Corbyn insisted "the Scottish party is not going to split off from the UK party", and said he would continue to work with Ms Dugdale despite her support for Mr Smith.
But he said it was "a matter for the Scottish Labour party" whether Ms Dugdale faced a leadership challenge in the future.
Mr Corbyn added: "I'll be happy to work with her after this election and we will work together because we're in the same party, we're in the Labour Party, we want to see a better society."
Earlier, former Labour advisor Paul Sinclair claimed in an interview with BBC Scotland that Ms Dugdale could face a challenge from her deputy, Alex Rowley, if Mr Corbyn continues as UK Labour leader.
Mr Rowley is backing Mr Corbyn in the leadership contest, as is former Scottish Labour leadership candidate Neil Findlay.
But Mr Rowley insisted a leadership challenge was "absolutely not on the cards" and said suggestions he wanted to replace Ms Dugdale as leader were "rubbish".
And Mr Findlay said there was "absolutely no way" he would consider standing again, adding that Ms Dugdale had a "very large mandate to lead the Scottish Labour party".
Thursday evening's debate saw Mr Smith claim Labour had "gone backwards" in Scotland under Mr Corbyn, with the party finishing third behind the SNP and Conservatives in May's Holyrood election.
Mr Corbyn said the party had to do more to challenge the "austerity" of the SNP government, but admitted Labour was facing a "big fight ahead and a long road back".
Mr Smith is attempting to unseat Mr Corbyn less than a year after he was overwhelmingly elected as leader.
The leadership contest was triggered after dozens of Mr Corbyn's frontbench team - including then-Work and Pensions spokesman Mr Smith - quit in the wake of Hilary Benn's sacking on 26 June.
The result is due to be announced on 24 September.
Jeremy Corbyn has urged Labour members to show "respect" to the party's Scottish leader after she was jeered at a hustings debate in Glasgow.