"If only they had asked me if I would take your place, I would have done so willingly, leaving you this world to grace," she said.
"You should have had so many years to watch your life unfold, and in the midst of this watch me, your devastated Mom, grow old."
Echoing the words of the poem, she told how she had been left with an ache "deep down" inside.
Mourners packed into pews as the teenager's classmates carried the coffin bearing his 6ft 2in frame into the chapel.
Andrew died at his home in Crooksling at the foot of the Dublin mountains just a week ago when a car he was working on collapsed.
Last night, classmates from Clongowes College, where he was a boarder, formed a guard of honour for his funeral cortege making its final slow journey, up the long driveway to the school.
As the cortege emerged from the darkness of the school grounds into the courtyard, lit by a single light, Andrew's parents and sister Sarah May were greeted by friends and relatives.
Derry and Sallyanne Clarke clung to each other when the coffin was taken from the hearse and carried by six of Andrews classmates to the door of the Boys Chapel.
Clongowes Rector, Fr Michael Sheil, received the remains and performed a blessing.
Inside, the church was packed and hundreds were accommodated in an area of the college to the left of the church where they watched the service on three large screens.
Andrew's sister Sarah May (22) walked with her parents behind the coffin clutching a photograph of her dead brother.
As the coffin was placed before the altar, Andrew's grandmother, Sadie, placed a copy of the Gospels on top.
Fr Sheil compared Andrew's life to the beautiful short life of a butterfly and urged mourners to celebrate "that he lived among us for 16 years".
Clongowes school choir sang hymns throughout the service.
Fr Sheil told mourners that Andrew's heart, lungs, kidneys and liver had all been donated to save lives.
He asked everyone not to send flowers, but instead make donations to Strangeboat Organ Donors Foundation, which is a voluntary organisation set up to encourage organ donation and support families of those who die.
Andrew's funeral Mass was being celebrated today by Clongowes School Principal Fr Leonard Moloney, followed by burial at Mount Jerome Cemetery.
Andrew died on New Year's Eve, a time when the family would normally be celebrating with an annual holiday at Ashford Castle in Cong.
This week the teenager had been due to fly to Birmingham to collect his trophy for 3rd overall place in the Irish Junior Ginetta Championships.
A motor enthusiast, he was heavily involved in the championship along with Junior Rallycross and Motor Sports Ireland.
He was a well-know figure in Mondello Park, which is close to the school he referred to as his second home.