Michael Gething, 42, died near the Methodist Church in Totnes. It is believed he died of hypothermia.
Mr Gething is thought to have been living in the town for about 18 months.
South Hams District Council said it would be assessing whether any premises in Totnes might be suitable for a shelter or hostel.
Local undertaker Rupert Callender, who arranged the funeral, said: "I hope people might put their judgements aside about what life on the streets is like, and what people who live on the streets are like.
"I hope they can see that they are ordinary people who have fallen on hard times."
Jonathan Taylor, who took part in the funeral proceedings, said: "There is a sense that this is a really important community event."
Melissa Worsley, who lives in Totnes, said people such as Mr Gething "are part of the community and we should look after them".
She added: "If they can't cope with society they still have the right to be looked after."
Earlier in the week Graham Walker, who used to be homeless in the area, slept out for 48 hours to raise funds towards Mr Gething's funeral.
Mr Walker said: "He died on the street. I think that, as a community, we should be aware of that fact and acknowledge it, and do something about it."
South Hams Council said it was saddened by the death of Mr Gething, adding he had been offered advice, assistance and accommodation on several occasions.
It added: "Unfortunately, accommodation is not always available in Totnes and sometimes it may be offered in nearby towns.
"A place was offered to Mr Gething in a supported accommodation unit in Dartmouth, known as St Barnabas, but he did not take up the place."
The council added that, in the event of severe weather, it had an emergency protocol in place which sought to ensure people living on the streets were offered help and accommodation.
The coffin of a man who died while sleeping rough on the streets of a Devon town has been carried by local people during his funeral.