Shipman murdered 215 of his patients using the drug Diamorphine over a period of 20 years.
But he claims no one saw him do anything in the letters, which are analysed in a BBC One documentary in the North West region tonight.
In one letter he says: "No one saw me do anything. As for stealing morphine off the terminally ill, again no one saw me do it."
In another he says: "The police complain I'm boring. No mistresses, home abroad, money in Swiss banks, I'm normal. If that is boring I am."
Psychologist Dr David Holmes says Shipman's letters show he relished the attention of being Britain's most prolific serial killer.
The doctor told the programme that Shipman thought he was a "medical god".
He said: "He saw no one as being superior to him. In
his own mind, in his own eyes, he was some sort of medical god."
Shipman died in January 2004 after hanging himself in his cell at Wakefield Prison.
Senior judge Dame Janet Smith led an investigation into the doctor's killing spree.
She recommended changes to the structure of the General Medical Council (GMC), tighter access to controlled drugs and reform of death certification to make it less open to abuse.
But she told the programme she was "disappointed" that key recommendations from her report had not been achieved.
She said: "We haven't moved at all on the basic death certification. It's exactly the same. There hasn't been any further work done since I moved off it in 2003."
More stringent cremation forms were introduced in January last year but there is still no unified system covering all deaths, as Dame Smith recommended. Revalidation, an "MoT" of a doctor's fitness to practise, also has not been introduced.
Barry Swann, whose aunt and mother were both killed by Shipman, told the programme: "It would be a travesty after all that we have been through if there were still loopholes."
But GMC chief executive Niall Dickson said progress had been slow because doctors feel threatened by change.
He said: "Part of the reason is convincing the profession that it is a good idea, and I think that we have begun to do that. But I think it has been a slow process.
"And I certainly think some older doctors found it a threatening process."
In a statement to the programme, the Department of Health said the majority of recommendations from the Shipman Inquiry have now been implemented.