Father-of-two Bird first killed his twin David before going on a shooting spree in west Cumbria.
Yesterday their local vicar the Rev Jim Marshall, curate of St Michael's Church in Lamplugh, said the family had no idea why Bird flipped.
Mr Marshall said: "If they had the strength to do it, they were the sort of people who would have gone round to each one of the (families of) people killed and wounded to apologise. That is the strength of their feelings.
"Having said that their brother, their father and son is a person who in all sorts of respects still has their respect because he's not the person they saw and heard about on Wednesday.
"For 52 years they see one man, for several hours they heard about another."
Mr Marshall also read out a short statement on behalf of the killer's sons Graeme and Jamie.
It said: "We are utterly devastated about the death of our father Derrick Bird. To us, he was the nicest man you could ever meet.
"We would like to say that we do not know why our dad committed these horrific crimes. We are both mortified by these sad events.
"Dad was a loving and cheerful character and was well-known throughout the whole community and in the areas where he worked.
"He will be missed by us, by his family and friends."
They sent their condolences to their father's victims.
Bird's elder brother Brian also issued a statement saying: "The loss of both my brothers is devastating. They were both very caring, family people. They were well known and respected in their local communities.
"My family and I are saddened at the loss of life and woundings and can only offer our condolences to the families concerned.
"We appreciate what they are suffering at this time. We cannot offer any reason why Derrick took it upon himself to commit these crimes."
In the early hours of Wednesday self-employed taxi driver Bird claimed his first victim. It is thought a simmering grudge against his twin brother over money left by their late father Joe sparked the mass killings.
Joe Bird gave David 25,000 before he died in October 1998 at the age of 82.
Police also confirmed the taxman was investigating Bird and friends have spoken about a mystery 60,000 in his bank account.
After blasting his brother to death at his home, Bird went on to target others with whom police believe he may have had bitter feuds in the past.
He killed family solicitor Kevin Commons and then pumped bullets at his fellow cabbies outside the rank in Whitehaven, claiming the life of Darren Rewcastle.
He went on an hour-long rampage killing random passers-by. However last night details emerged of another man who was seemingly on Bird's hit-list but had a lucky escape.
Neighbours of Jason Carey – who went scuba diving with Bird – said the killer banged on his front door. But Mr Carey, who lives in Wilton, had been on the night shift and did not answer.
After failing to rouse Mr Carey, Bird continued driving, firing his shotgun and .22 rifle from the window of his taxi.
A frantic police manhunt only ended when Bird took his own life in remote woodland after abandoning his car.
Details of funerals for Bird and his victims are still not clear.
Mr Marshall said the family had at one stage considered a joint funeral for the twins, but this had been dropped.
Yesterday police said they had seized reams of paperwork and a computer from Bird's home.
But because Bird apparently left no suicide note investigators remain in the dark about why he embarked on the attacks.
The other victims were Kenneth Fishburn, 71, Susan Hughes, 57, James Jackson, 67, Jennifer Jackson, 68, Isaac Dixon, 65, Michael Pike, 64, Jane Robinson, 66, Jamie Clark, 23, and Garry Purdham, 31.
HUNDREDS BRAVE RAIN FOR SERVICE
More than 400 people braved rain yesterday to remember those that died in Derrick Bird's shooting spree across west Cumbria.
An open-air service took place at Seascale where taxi driver Bird killed Michael Pike, 64, Jane Robinson, 66, and Jamie Clark, 23. In nearby Gosforth, he blasted Garry Purdham, 31.
People of all faiths
wore waterproof jackets
and huddled under umbrellas to listen to the hour-long service.
Afterwards, the minister at Seascale Methodist Church Rev Philip Peacock said: "We wanted to be outside so that the service was accessible to everyone – irrespective of the weather.
"We chose here particularly because this road (Drigg Road) was where so much tragedy happened."
Another service took place last night at St Nicholas' Church in Whitehaven, where cabbie Darren Rewcastle died.