Twenty-nine-year-old Leo Seemanpillai had been living in the community on a bridging visa in Geelong prior to his death, which is believed to be self-inflicted.
The Sri Lankan asylum seeker was flown from Geelong Hospital to The Alfred hospital in a critical condition, where he later died on Saturday.
Addressing media on Monday, Mr Morrison said Mr Seemanpillai had been granted a bridging visa since his arrival in Australia in January 2013, but an application for a protection visa remained pending.
He said the man had been receiving mental health support and had been visited by a case worker the Friday prior to his death.
When asked if he would take responsibility over the incident as Immigration Minister, Mr Morrison replied that it was a "terrible and tragic" occurrence.
Tamil Refugee Council spokesman Aran Mylvaganam has told Fairfax Media that Mr Seemanpillai was fearful of being sent back to Sri Lanka, where he would face "persecution from the military."
"He's been in limbo ever since he got here in terms of his visa situation, and this coupled with his depression and fear of being sent back," Mr Grant said.
People have left tributes to Mr Seemanpillai on the Council's Facebook page, describing him as "someone's son, brother, friend".
"The fear of being sent back to persecution in Sri Lanka drove him to this act of self immolation and it will not be the last," one commenter posted.
"Without permanent protection, people have no assurance of their ongoing safety. With no allowance for family reunification, their loved ones continue to suffer human rights abuses in their homelands. This forces asylum seekers to live in constant despair and without any hope for the future."
A memorial service will be held for Mr Seemanpillai this Friday from 6pm at St Mary's Catholic Church, High Street Thornbury.
The service, which will be held in Tamil and English, is being organised by the Darebin Ethnic Communities Council and the DASSP-Darebin Asylum Seeker Support Project.
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14 or Suicide Call Back Service 1300 659 467.
With AAP.
