Speaking atop Ireland's holiest mountain, Croagh Patrick in County Mayo, Neary was joined by an estimated 12,000 pilgrims including Archbishop Charles Brown, papal nuncio, for the traditional ascent of the 800-metre mountain where St. Patrick fasted for 40 days in the fifth century.
Brown, the first papal nuncio to Ireland to complete the grueling climb, spent about five hours on the mountain chatting to pilgrims and hearing confessions.
Referring to the clerical abuse scandals that have rocked the Irish Church, Neary said "on this mountain of St. Patrick in the year of the eucharistic congress in Ireland perhaps we might see the beauty in the rich inheritance of our faith despite the shadow of recent darker days."
Underlining the devotion of Irish Catholics during centuries of persecution when the celebration of the Eucharist was illegal, Neary said "our ancestors were not gullible people who risked their lives as they made their way to some hidden glen to gather around the Mass rock. They felt deeply the need to celebrate the Eucharist. Their strength lay in their closeness to God and to each other."
"They learned their prayers around the fire and turned to God in those same words in days of joy and nights of pain, sorrow and loneliness," he said.
He urged Irish Catholics to be more upbeat, insisting "there is so much good here that has been swallowed up in criticism."
"There is still a vibrant faith expressed in the many people who trek to daily Mass, those who go out to care for the poor and all those who direct their energies to deprived children and the forgotten elderly."
Neary also said the Church had to be present to reach out to Catholics who no longer practise the faith.
"Looking down from the summit of Croagh Patrick today we can see again a beautiful country and a revitalized Church stretching her arms out to all who want to come home," he said.
"Some, sadly, in these days do not find any attraction in their faith. They may have abandoned the Mass because they find it repetitive, structured or as many people describe it as boring. Maybe this is because we have emphasised too often the ritual and rubrics or the notion of celebration without drawing attention to the task or mission of the Mass," Neary said.
The climb, which has been carried out uninterrupted for more than 1,500 years, saw many pilgrims walk barefoot.
However, organizers and local clergy discourage the practice on health and safety grounds.