In a statement read to the Manchester hearing, Mr Burgess said: 'I loved her so much. She was a beautiful baby.'
He said he was afraid to put her down on the night she died because she was wheezing and suffering from wind. 'I must have dozed off with Natalie in the crook of my arm,' he said.
Mr Burgess and his girlfriend Helen Anderson of Longsight, Manchester, were taking it in turns to care for the baby on the night she died in April.
Just after midnight Ms Anderson fell asleep. Mr Burgess fed the baby at 1.45am and dozed off while watching television, with her in his arms.
Ms Anderson raised the alarm when she awoke two hours later and saw her daughter was motionless. 'She felt cold and I looked at her and thought, God she looks a bit white. When I picked her up her arm just flopped and I thought there was something wrong.'
At first police treated the death as suspicious and the couple were questioned for two days.
Dr Anthony Barson, a pathologist, said Natalie's head injury had probably been caused by pressure. He agreed with the coroner that, 'if the baby was in the crook of the father's arms and he leant on her with his whole weight, the baby might have sustained the bruise that way'.
The coroner, Leonard Gorodkin, said: 'There is nothing suspicious about Natalie's tragic death.' He recorded verdict of accidental death.