His parents, Tom Evans and Kate James, had been at the centre of a High Court battle as they attempted to challenge a court ruling allowing Alder Hey Children's Hospital to withdraw ventilation, after doctors said continued treatment was "not in Alfie's best interests".
Doctors believed Alfie had a degenerative neurological condition, which has led to parallels being drawn with the case of Charlie Gard.
His coffin sported images of toy soldiers and the Everton club motif.
Alfie had a degenerative neurological brain condition and his case drew worldwide attention when his parents became determined to keep him on life support.
Earlier, members of Alfie's Army tied purple and blue ballons to the Dixie Dean statue outside the stadium and a bow in the same colours to the gates behind.
Hassan Says Rollback of Net Neutrality Rules Could Hurt NH's Dairy Farmers
Without congressional action to overturn the FCC's decision, the old net neutrality rules expire June 11 . Ultimately, it would require President Donald Trump's signature, or enough support to override a veto.
A private funeral for 23-month-old Alfie Evans will be held next week, it has been announced.
The terminally ill toddler, who was in a semi-vegetative state from a degenerative condition that medics were not able to definitively identify, died in hospital on April 28.
In February, a High Court judge ruled that doctors could stop providing life support for Alfie, against his parents' wishes, saying the child required "peace, quiet and privacy".
A separate vigil was held in Liverpool's Springfield Park last Wednesday to mark what would have been Alfie's second birthday. His parents, Tom Evans and Kate James, had lost a lengthy legal fight that went to the European Court of Human Rights. Alfie's parents had also wanted to fly their son to Italy for further treatment.