He claimed that her son, David Methven, had threatened to kill him if he went to the police.
Kean, who denies murdering the pensioner at her home in Forteviot, Perthshire, on February 20, was giving evidence on the eighth day of the trial at the High Court in Glasgow.
He told defence QC Brian McConnachie he took his son to school on that date and then went to Mrs Methven's cottage to collect paperwork and two tyres Mr Methven had left there for him.
The court was told Kean and Mr Methven were friends and involved in business together.
Kean said he phoned Mr Methven who told him his mother had a doctor's appointment and would be back at 11am.
The jury of nine women and six men was told by Kean that he pulled into a lay-by and had a cup of coffee from a flask and then drove to Bridge of Earn to waste time.
He said he arrived at the cottage at 10.50am and went to the back door, which was open.
Kean said: "I knocked on the door and got no answer and I shouted: 'Mrs Methven, Mrs Methven'."
He was asked by Mr McConnachie: "Did you get any response?" Kean said: "No."
The court was told Kean went into the living room and then into the kitchen, where he saw Mrs Methven lying on the floor.
Kean said: "I thought she had just fallen. I went forward into the kitchen and noticed there were towels on her head.
"I bent down and said: 'Mrs Methven, what's happened to you?' All I heard her say was 'David, David'. That's all I could make out – 'David' – but nothing else."
Kean was asked what he did and replied: "I said 'Mrs Methven, I'll get you on to a chair and I'll get you a drink of water'."
He said Mrs Methven was unable to take the water and he drank it himself, before putting the tumbler into the sink.
The defence QC asked: "Why did you not phone 999?" Kean said: "When she said 'David, David' I thought 'has he done something to her' and because I was on my own I panicked and thought I would get the blame."
Kean was then asked why he did not dial 999 and just not give his name. He replied: "I didn't know I could do that. I do regret not phoning the emergency services. There is no excuse for that."
He was asked what he did then and replied: "I looked at Mrs Methven and just left the house."
The court was told Kean then drove to Broughty Ferry, where he had a cup of coffee and chatted to two of his workmen.
Later that day he gave his niece a driving lesson.
Mr McConnachie asked him how he could carry on as normal and Kean said: "I wasn't feeling great during the day, but I didn't like to ever let anyone down."
The defence QC then said: "But this was an extraordinary day. You have discovered a good friend's mother injured and possibly assaulted in her home. How could you carry on as normal?"
Kean said: "I tried not to show any emotion that day, but I was quite cut up by it."
He was asked why he did not go to the police when it became known Mrs Methven had been murdered, and said her son had asked him not to.
Kean claimed he went for a coffee with Mr Methven at a cafe in Perth on March 16.
Kean said: "He told me I would probably be interviewed by the police. He said 'whatever you tell them, don't say you were at the house that day'."
Kean claimed Mr Methven told him he knew who had killed his mother. He added: "He said it's druggie friends, but it's all sorted. He told me he would have me done in if I opened my mouth."
During cross-examination by prosecutor Alex Prentice, QC, Kean, who was once a special constable with Tayside Police, called for the killer of Mrs Methven to "come forward as soon as possible".
Kean has lodged a special defence blaming Mr Methven for the death.
The trial continues.
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