Paying tribute to Mr Lambert, Mr Cullen said Mr Lambert had animated and intrigued generations of Irish children.
“Eugene Lambert was a master of the art of puppetry and his place in Irish theatre is unparalleled, both in the quality and uniqueness of his work as a puppeteer and ventriloquist and for the longevity of his contribution,” said Mr Cullen.
“Eugene was a natural storyteller whose words were entertaining and accessible to his young audiences.” said the minister.
Mr Lambert, 82, a father of 10 who died unexpectedly in his home in Monkstown, Co Dublin, on Monday night, was due to celebrate his 60th wedding anniversary with his wife, Mai, this summer.
The star of TV show Wanderly Wagon that ran from 1967 to 1982, counted the late pop star Michael Jackson among his many fans.
Jackson befriended the veteran puppeteer after a concert in Dublin in 1992 and visited him again with his three children on his birthday in August 2007.
Mr Cullen said Mr Lambert was founder and director of the Lambert Puppet Theatre and the inspiration behind Dublin’s International Puppet Festival.
“As Ireland’s only festival dedicated to professional puppet theatre, it developed under his guidance strong national and international respect over the years by presenting the highest calibre professional companies performing for families and children,” said Mr Cullen.
His granddaughter, Emily Tully, whose mother, Miriam Lambert, voices and manipulates Bosco, the red headed cheeky puppet, said Mr Lambert’s death had come as a huge shock.
Ms Tully said her grandfather had never really retired and was still working on entertaining children because he never wanted to do anything else.
“He’s left a real legacy; he was a legend really,” she said.