A local resident has set up a charity to help raise funds for the family.
Police are continuing to question a man and a woman arrested on suspicion of murder.
The woman, 28, and man, 38, from Derby, were arrested separately on Friday.
The children have been identified by police as 10-year-old Jade Philpott, John Philpott, nine, Jack Philpott, seven, Jessie Philpott, six, and Jayden Philpott, five.
Their 13-year-old brother, Duwayne Philpott, who was also in the house in Victory Road, remains in a critical condition in a Birmingham hospital.
Prayers for the children were read at a special service held at St George's Roman Catholic Church, which is affiliated to the school the children attended.
The Reverend Alan Burbidge, chair of governors at the St George's Catholic Primary School in Littleover, said staff had been trying to comfort pupils.
End Quote Karen Hillier Local councillorI think it's been a shock and the reality is just starting to set in now ”
She said: "In times like this when the emotion is felt it brings people together more.
"I think it's been a shock and the reality is just starting to set in now as well."
Local resident Bobby Sutherland, who has lived in the area all his life, said he was inspired to set up an online charity called Catch Me When I Fall to help pay for the funerals and anything else the family might need.
Mr Sutherland said: "I said to my missus they're going to have to pay about £10,000 when they get home - and that ain't right."
He added that Mr Philpott "loved his children desperately".
Gavin Tomlinson, area manager for Derbyshire Fire and Rescue, said the parents had managed to get out of the house and were trying to get to the children, who had been asleep upstairs when the fire began, when fire crews arrived.
Temporary Assistant Chief Constable of Derbyshire Police Steve Cotterill said: "There appears to have been some valiant attempts by the father [Mick Philpott] to resuscitate his children."
Mr Philpott, who was named locally, is believed to have 17 children.
His family were the subject of media scrutiny in 2006 when he asked the council for a larger house to accommodate his wife, girlfriend and 14 children.
In 2007 former Conservative MP Ann Widdecombe spent a week living with the family as part of an ITV documentary and he also appeared as a guest on the channel's Jeremy Kyle Show.
Appeal for information
Following the fire Miss Widdecombe said: "Nobody would ever call him a bad father. I'm so sorry to hear the news and my thoughts are with the family."
Post-mortem tests are due to take place later and forensic specialists continue to examine the house.
Mr Cotterill said eight people were living in the house on a permanent basis, though other people may have stayed there on an ad hoc basis.
He said: "I want to stress that we are keeping an open mind in terms of the investigation - the arrests are only one aspect of the inquiry.
"It is paramount that we have a thorough investigation of the scene before we determine the cause of the fire.
"Our thoughts are with the parents and the family of the children for their tragic loss and for the community of Allenton, who would of course have known the children as they played."
Anyone with information about the fire has been asked to contact Derbyshire Police.