Tom Evans and Kate Jones said they were “heartbroken” after the terminally ill youngster died in hospital at 2.30am on Saturday.
They had launched a series of legal challenges to continue treatment for their 23-month-old son, who had a degenerative neurological condition.
The Pope, who gave Alfie and his parents Italian citizenship as they tried to win permission to move him to Rome for treatment, said: “I am deeply moved by the death of little Alfie. Today I pray especially for his parents, as God the Father receives him in his tender embrace.”
Hundreds of people gathered outside Alder Hey Hospital in Liverpool, where the youngster had been treated, on Saturday afternoon to release balloons in his memory.
Others left flowers outside the medical centre, with messages such as: “We fell in love with a little boy we never knew. Alfie will be forever engraved in our heart. Fly high little man”; and “Alfie you stole the heart of the world!”
Many were seen crying as they visited a scene where, on Monday, as passions ran high, police were forced to block dozens of people who tried to storm the hospital building.
Thousands paid tribute on social media, with RIP Alfie Evans trending all morning, but their comments were often highly polarised over the courts’ decisions.
His story also featured heavily in news bulletins and on websites around the world.
On Saturday morning, Kate Evans broke the news on the Alfie’s Army Facebook page, saying: “Our baby boy grew his wings tonight at 2:30 am. We are heart broken. Thankyou everyone for all your support.”
Tom Evans said on the social network at around the same time: “My gladiator lay down his shield and gained his wings at 02:30 absolutely heartbroken. I LOVE YOU MY GUY.”
In February, Mr Justice Hayden ruled that doctors at Alder Hey could stop treating Alfie against the wishes of his parents.
The couple, from Liverpool, wanted to move their son from the city’s Alder Hey Children’s Hospital to Italy where they said doctors were willing to treat the little boy.
The judge said he accepted medical evidence which showed that further treatment was futile.
Court of Appeal judges upheld his decision, while Supreme Court justices and European Court of Human Rights judges refused to intervene.
Alfie’s life-support machine was switched off on Monday night.
On Tuesday morning, Mr Evans said doctors were “gobsmacked” that his son was breathing nine hours after his life support ended and the couple went back to court in a bid to get permission to take him to Rome.
Mr Justice Hayden said the family could instead “explore” the options of removing him from intensive care either to a ward, a hospice or his home.
On Friday, his parents said they would work with doctors to ensure their son had the “dignity and comfort he needs”.
The public nature of the family’s fight with doctors has led to the case being a cause celebre for some groups.
Hospital bosses said they were “shocked” at the “barrage” of abuse received by some members of staff.
Merseyside Police felt it necessary to issue a warning over comments being made about the hospital online.
Archbishop of Liverpool, Malcolm McMahon, referred to the heated arguments taking place in a statement he made on behalf of the Catholic Bishops’ Conference of England and Wales.
He said: “I would like to express my deepest sympathy at this moment of loss to Tom and Kate as we hold little Alfie in our prayers.
“All who have been touched by the story of this little boy’s heroic struggle for life will feel this loss deeply. But as a Christian Alfie has the promises of God, who is love, to welcome him into his heavenly home.
“Although the past few weeks have been difficult with much activity on social media, we must recognise that all who have played a part in Alfie’s life have wanted to act for his good, as they see it.
“Above all, we must thank Tom and Kate for their unstinting love of their son, and the staff at Alder Hey Hospital for their professional care of Alfie.
“Now it is time for us to give Tom and Kate space to grieve their son’s death and offer our prayers for him and consolation for all.”
Alder Hey hospital said in a statement: “We wish to express our heartfelt sympathy and condolences to Alfie’s family at this extremely distressing time.
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“All of us feel deeply for Alfie, Kate, Tom and his whole family and our thoughts are with them.
“This has been a devastating journey for them and we would ask that their privacy and the privacy of staff at Alder Hey is respected.”