Eight-year-old Riley Holt, brothers Keegan Unitt, six, and Olly Unitt, three, died in the blaze on Sycamore Lane in the Highfields area of Stafford, alongside their sister, four-year-old Tilly Rose Unitt.
A fifth child, named locally as two-year-old Jack, escaped from a first-floor window along with his mother Natalie Unitt and her partner Chris. They remain in hospital with non-life-threatening injuries.
Teachers described the children as "bright, happy, loving and lively".
Nicola Glover, head teacher at Castlechurch Primary School said: "Our entire school community is absolutely devastated by this news.
"Riley was a very confident, excitable member of school who came every day full of enthusiasm. He was a caring friend who hated to see anyone hurt or upset and would do his best to help or cheer them up.
"Riley had a great sense of humour and an infectious giggle. He was a very bright and articulate boy who showed interest in all areas and was always keen to ask lots of questions.
"Tilly was a happy little girl who loved coming to nursery. She was a friendly and caring child who loved to read stories, dress up and paint.
"Tilly was always proud of her achievements.
"Olly was a happy, loving boy who loved cuddles. He was always happy to come to nursery and loved to be in the roleplay area with the dolls."
Kim Ellis, head teacher at Marshlands Special School where Keegan was a pupil, said: "Keegan was lively, full of fun and mischief with a really endearing smile.
"He loved school and everyone who worked with him loved him. We were all proud of him and the progress that he had made.
"It is very hard to accept what has happened."
Both schools said support systems were being put in place to help staff and pupils.
Floral tributes have begun being laid near the scene, while thousands of pounds has already been raised through crowdfunding to help support the family.
A handwritten note attached to a cuddly toy read: "RIP Babes xx life is so so cruel. All our thoughts are with the family at this very sad time."
One note read: "Will be dearly missed, love Uncle Dave and Auntie Lou Lou", while another added: "To my lovely grandkids I will always miss you. Love you always xxx"
An ambulance service dispatcher was among those paying their respects with a bouquet.
A note taped to the flowers said: "RIP you beautiful angels. I don't know you personally but I was involved in last night's incident.
"I am so gutted we couldn't save you all. I hope your family can remain strong and you will remain in everyone's hearts forever."
A nearby resident described how a sheet of flames engulfed an upstairs window at the semi-detached property, at around 2.40am on Tuesday.
The witness, who asked not to be named, told the Press Association at the scene: "We heard a bang and looked out of the back window upstairs.
"At the start it was just a sheet of fire coming out of the bedroom window. It seemed to take ages for the fire brigade to arrive - it seemed like forever.
"The neighbours came out and drove their car out of the back garden and there were lots of fire engines and police."
Local woman Amanda Blagg visited the scene to lay flowers and a teddy in memory of the children.
Wiping away tears, the 38-year-old told reporters: "I saw the mum every day at the school - her son is in the nursery with my son.
"I heard what had happened on the news and I just cried straight away. It's awful."
Another resident, who was also reluctant to give her name, said she had not realised that anyone had died in the blaze until she heard a news broadcast confirming that four children had died.
"The room at the back was completely full of flames," the woman said.
"We just stood there with our hands over our mouths wondering what was going to happen next.
"A man and a woman got into an ambulance. They were in blankets and she had the little one in her arms.
"I'd assumed they had all got out. It's terribly sad, almost beyond belief."
Fire crews remain at the scene combing for clues as to what triggered the blaze.
Part of the roof has collapsed, with the windows smashed and the inside appearing to have been blackened by smoke.
Speaking from the scene, Rob Barber, deputy chief fire officer for Staffordshire fire and rescue service, said: "One male, one female and a baby had escaped from the property prior to our arrival via a first-floor window.
"Our firefighters were faced with very difficult conditions inside the property due to the severity of the fire.
"At this time I cannot comment further on the likely cause."