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.

Ben Hooper started his 2,000-mile (3,200 km) swim from Dakar harbour in Senegal, west Africa.
Mr Hooper's four-month attempt is due to end in Natal in north-east Brazil, next March.
The 38-year-old long-distance swimmer from Cheltenham is hoping his sponsored Swim The Big Blue challenge will raise Â£1m for charity.
Other people have attempted the swim, but were not ratified by Guinness World Records.
French swimmer Benoit Lecomte was credited as the first to swim across the Atlantic without a kickboard in 1998, but this was not verified.
Mr Hooper said he faces hazards such as storms and ocean predators.
"The idea is to get across safely and I think my only real fear is if something goes mechanically wrong with me.
"Beyond that I am not too worried about marine life. I am going into their world, so I need to be respectful," he said.
"I've already met sharks and jellyfish and nothing has eaten me yet."
Mr Hooper is swimming freestyle front crawl for up to 12 hours a day, and will have to eat 12,000 calories a day to maintain his strength.
He is accompanied by two support boats.  The crews include a medic, body therapist and an official observer who will be reporting back to Guinness.
Nigel Taylor-Schofield, captain of one of the support vessels, said before the swim: "There are not many 'firsts' left in this world and I am looking forward to helping Ben join that exclusive and elusive club."
Mr Hooper has completed 12 million metres (7,456 miles) of ocean and pool swimming in preparation.
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.
[NEXT_CONCEPT]
A man has set off in a bid to set the first official world record for swimming across the Atlantic Ocean.