Hannah Thomas-Jones, who was 14, died in her sleep from the fumes while camping in Bucknell, Shropshire last May. Her 11-year-old brother Ben, mum Danielle, 30, and stepdad Phil, 49, survived.
Shropshire Coroners' Court was told that the barbecue had been put in the tent to keep the campers warm, and that they were unaware of the dangers.
The family, from Wilmslow, Cheshire, had been camping at the Baron of Beef campsite with relatives.
Danielle Jones, Hannah's mum, said they had used the barbecue underneath a gazebo and then moved it into the porch of the tent.
Mrs Jones sobbed as she told the court they had never used it before and decided to take it into the porch after it had 'blown down and wasn't smoking'.
"I was worried about fire risk so we took the lid off the cooking stove and we placed that on the floor of the tent and made sure it was fire proof," she explained, "We moved it out of the way of the walkway to make sure nobody would trip over. Obviously we didn't understand the dangers of the carbon monoxide."
The devastated mum said she put Hannah and Ben to bed at around 10pm and they went to sleep in the left-hand compartment in the tent.
"I gave them both a kiss, Hannah was sat up, on her phone at the time, on Facebook normally," she said. "I stayed up until about 11.30pm and we decided to go to bed in the tent."
Mrs Jones said when she woke in the morning her arms and legs felt sore and she could not talk, and after hearing a 'lot of shouting' and the tent being opened at both sides, she was told by paramedics Hannah had died.
The Mirror reports that pathologist Dr Cerys Burrows found lethal levels of carbon monoxide in Hannah's blood during her post mortem.
Coroner John Ellery recorded a verdict of accidental death, and said it was a 'tragedy'. He added that he hoped that the inquest would help raise awareness of the dangers of carbon monoxide.