The body of Owen Creaney, 40, from Victoria Place in Lurgan, was found in a wheelie bin in the porch of a house in Moyraverty Court on Saturday.
A 23-year-old woman and a 27-year-old man are being questioned about his death.
Monsignor Aidan Hamill said the family was distraught by what had happened.
"They're very upset and distraught that this awful thing has happened to them," the parish priest at St Peter's in Lurgan, said.
"They have the support of their family, but nevertheless in spite of all of that, it's the most upsetting thing to happen to any family to have to go through.
"It must be a horrendous ordeal for them to have to go through this knowing the awful things that happened to him.
"I don't know the details myself, but the fact that it happened and the way that it happened is making it an awful experience for them to have to live this."
Police said Mr Creaney, who was disabled and used a walking aid, had been the victim of a sustained assault.
They described him as a "frail and vulnerable" man who had only recently celebrated his 40th birthday.
At a news conference on Sunday, police said they believed Mr Creaney had been assaulted and had appeared to survive, but died some time later.
His body was found in the bin at the house where the 27-year-old man lived.
Police investigating Mr Creaney's murder were granted additional time on Monday to question the man and the 23-year-old woman.
They were both arrested on Saturday, but can now be detained until Tuesday.
Neighbours told the BBC the man who was arrested had only moved into the area three weeks ago and they believed the body may have been there for a number of days.
Monsignor Hamill said Mr Creaney's death had shocked the local community of Lurgan.
"People are horrified, upset, angry that this kind of thing has happened, but generally people can't believe that such a horrendous incident happened to a member of our community," he added.
The cause of Mr Creaney's death will not be released until a post-mortem examination has been carried out, the PSNI said.
Police have appealed for anyone who saw anything suspicious around Moyraverty Court between Wednesday and Saturday afternoon to contact them.
The parish priest of a family whose son was murdered in Craigavon has described what they are going through as a "horrendous ordeal".