Local man Robert Corbet, from Portlaoise, Co Laois, was remanded in custody after appearing in court charged over her death.
Corbet (24) was accused of murdering the 30-year-old nanny on October 25.
Aoife went missing after leaving her friend's home at Colliers View in Portlaoise.
She had been working in the town as a live-in nanny for a married couple.
Her funeral took place this afternoon at St Patrick's church, Ballyroan, in Co Laois.
In the same church on Thursday night, local people had attended a memorial Mass.
The Phelans said her death has left them "heartbroken".
"She was a loving daughter and sister and we will miss her dearly," they said.
Corbet, of Sheffield, Timahoe Road, runs a local haulage business.
He is charged with the murder of Ms Phelan at an area known as Capoley, which is just over a kilometre from where her body was found.
In a statement issued through local priest Fr Gerard Ahern, Aoife's family praised all those who have supported them.
"We are overwhelmed by the support and the kindness we have received over the past two weeks.
"We would like to thank all the people who helped in searching for Aoife and who have been there for us."
At Portlaoise District Court yesterday, Det Sgt John Healy said he formally arrested and charged Mr Corbet with murder at 11.27pm on Thursday.
In reply to the charge, Mr Corbet "shook his head and said 'No'," the court heard.
Up to 100 onlookers stood on Portlaoise Main Street as Corbet was brought before a special District Court.
He was remanded in custody to Cloverhill and will appear again in court on November 15.
After an application from a legal representative for Corbet, Judge Catherine Staines recommended that he receive psychiatric attention in Cloverhill.
An application for free legal aid was deferred until next week's court session.
The Phelans acknowledged the "efforts of An Garda Siochana who have worked tirelessly".