On the day of Billie-Jo's murder, Mr Jenkins, 40, told police he had not been in the family home for as long as 45 minutes before her body was found on the patio.
But he later described returning home after collecting a daughter from a music lesson and overhearing Billie-Jo in conversation only around 15 minutes before the death was discovered.
Billie-Jo, 13, was found bludgeoned about her head with a metal spike in February last year at the family home in Hastings, East Sussex, where she had been painting the patio doors.
Asked to explain why he had not given full details earlier in the investigation, Mr Jenkins said in interview that he did not know. "I pushed myself to give every bit of information to [DC Steven Hutt]," he said.
Lewes Crown Court heard that he initially said he had not gone into the house after the music lesson, but waited on the steps outside for his daughter Lottie to drop off her clarinet.
But under questioning four days later, he said: "I would have been aware if there had been anything wrong. I was aware that Billie was alive."
In statements read to the court, police were heard asking Mr Jenkins why he initially failed to observe the extensive savage injuries to her skull.
Detective Sergeant Anne Capon asked: "You find your daughter in a pool of blood, you go over to her, you think you notice a scratch on the side of her face, but you didn't notice a big gaping hole in the top of her head?" Mr Jenkins said no.
Mr Jenkins, who denies Billie-Jo's murder, said he must have been in shock.
The trial continues.Reuse content