Bedford Hospital's medical staff committee said Ken Williams was being made a scapegoat for what they described as "the chronic under funding of the pathology services".
Mr Williams resigned after it emerged that up to eight bodies were stored on the floor of a chapel at the hospital, wrapped only in sheets.
Relatives of the dead have spoken of their horror and some are seeking legal advice.
"We are concerned that any pressure is being put on him because at the end of the day he is not really responsible for the under funding that has led to this situation," he said.
"Although I hear the regional chief executive say that it is unacceptable I am not entirely clear what alternative Bedford Hospital, or indeed many other hospitals might have when they are faced with an overflow situation."
'Scapegoats'
He said hospital managers were being "scapegoated" out of "political expediency", adding that the money was available, but that managers were forced to spend money on cutting waiting lists and were not able to spend the money in the way they wanted.
"We see pathology as a priority but Mr Milburn [the Health Secretary] would rather it was spent on treating non-urgent cases within 18 months.
"We would rather see the money spent on people already in our care, whether dead or alive, than on people who are yet to be treated."
Bedford's Labour MP has claimed that the hospital has stored bodies in a chapel on several occasions despite claims by the management it was what they called a "one-off" incident.
Patrick Hall, told BBC Radio 5Live the chapel had been used to store bodies for several years.
"It's been going on for possibly some years," he said. "It's been a frequently occurring incident and it's totally unacceptable."
"There's been a complete lack, it would seem, of any proper procedures."
Mortuary full
The bodies were left in the carpeted, unrefrigerated room at the hospital for up to 24 hours at a time, after a mortuary was closed when problems with the doors led to a porter injuring himself.
An investigation by the hospital found the hospital had done the same thing in the past when the mortuary was full.
Peter Houghton, NHS Executive regional director of the Eastern region, said an investigation into the incident found the hospital had no policies in place for what should happen if the mortuary was full.
Mr Houghton said: "It appears that this has happened on rare occasions in the past when the mortuary was full.
"On this occasion, despite having a temporary mortuary available, bodies were stored on the floor in totally inappropriate conditions.
"The reason the additional temporary facility was not being used was because of problems with the doors, not because there were no places available."
Shadow health secretary Dr Liam Fox said: "The resignation of the chief executive does not remove the need for an independent inquiry.
"We have evidence that these practices have been going on for at least three years and that there are major management problems in this hospital which requires detailed investigation."