The debate, on Thursday, was discussing "serious and widespread failures" in Gloucestershire's children's service.
Cllr Shaun Parsons, chairman of the council, said members had been told the proceedings were being televised.
Two said they had been listening, one blamed medication, but the fourth admitted the meetings "drag a bit".
Mr Parsons said he believed the chairman's role is to make sure the meeting runs smoothly and efficiently but added it is not his place to "give councillors a nudge".
But the former MP for Stroud, Neil Carmichael disagreed. He said it was "wrong" that councillors fell asleep "during such an important meeting on such a critical subject".
"As chairman of the Commons Select Committee I felt it was very much my job to ensure that meetings were run briskly and that all those present were fully engaged throughout," the Conservative said.
Four councillors were spotted nodding off, including deputy leader, Conservative Ray Theodoulou who blamed his heart medication for making him "a little drowsy".
Fellow Tory Rob Bird said he may have "closed his eyes for a moment", while Liberal Democrat John Cordwell admitted he "might have nodded off very briefly". Both men insisted they were aware of the proceedings.
But Labour's Graham Morgan was more forthright though, stating: "Those meetings drag a bit and I'm 66."
Mr Parsons said although he had not seen the BBC film it was important to listen to what the councillors had said in mitigation.
"It was a very long day, people had been briefed quite considerably on the facts.
"But it's not a good appearance for people maybe to have been asleep or indeed nodding off... ,  it's most unfortunate."

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Gregory will tee off at Augusta National for the first time on Thursday after securing his place by winning the British Amateur Championship last summer.
Before even setting foot on the famous Georgia course, the 22-year-old from Waterlooville, Hampshire had his eyes glued to hours of footage from the past four years.
"I've watched a lot of clips on YouTube," he told BBC South Today. "I've got clips of all the pins from the past four years from every day.
"I know roughly where the pins will be as they don't change them too much from year-to-year. So, I've had a good idea of what kind of approach shots I need to work on in my practice rounds."
As well as staring at a screen, Gregory has also warmed-up for his Augusta bow with some on-course preparation.
Victory in the Georgia Cup over US amateur champion Curtis Luck following a play-off justified his decision to head out to the States three weeks before the Masters to acclimatise.
Along with Gregory and Luck, the three others amateurs competing at Augusta are Americans Brad Dalke and Stewart Hagestad, and 19-year-old Toto Gana from Chile.
Gregory is hoping for better fortunes than his mixed experience over two rounds of The Open at Royal Troon last July.
Having briefly held an early lead on four under par after 11 holes, he faded to shoot a first-round 78 and then missed the cut after a 73 in the second.
"I'm fortunate enough to have got all the excitement and hype of being at a major tournament out of the way," Gregory reflected.
"It's more normal now, so you just have to make sure you turn up and play golf and the sooner you get the thought of loads more people watching you, the easier it gets."
Gregory also hopes some wise words from 2013 US Open champion Justin Rose, who also learnt his trade as an amateur in Hampshire, will give him another invaluable Augusta insight.
"I'm hoping to pick up some tips from Justin," he said. "He's been great for my development being from the same area of the country and just seeing what he's gone on to achieve.
"I'm hoping to play the Par Three tournament with him before Thursday and he's out there doing what I want to do for the rest of my career."
The chairman of a meeting in which four councillors were filmed apparently dozing during has described their actions as "embarrassing".
[NEXT_CONCEPT]
They say you can learn almost anything on YouTube these days and Scott Gregory is hoping the video sharing website holds the secrets to a perfect US Masters debut.