Around 500 people were in the trade hall in Katowice for a pigeon exhibition when the roof caved in - possibly under the weight of snow.
The Polish ambassador in Ireland Witold Sobkow said it was a terrible tragedy.
“The only positive side to this is that it’s not a terrorist attack. This is just a tragedy because of a human fault, either because it was a construction fault or because someone neglected his duties and didn’t clean the snow from the roof.”
He said the 100,000-strong Polish community in Ireland had been watching the events on TVN 24, the Polish satellite news station, and phoning a specially set-up phone line for news of relatives.
Mr Sobkow said 66 people were confirmed dead and more than 200 injured, including foreigners who had been visiting the international pigeon fanciers exhibition.
“The last living victim was rescued at 10pm last night. It would be a miracle if we found anyone else alive now,” he said.
Taoiseach Bertie Ahern was among those who approached Mr Sobkow to offer his condolences at a diplomatic fundraiser in Dublin for the victims of the Pakistani earthquake.
A central section of the roof of the exhibition hall in Katowice collapsed at 4.30pm and a second collapse happened more than an hour later during rescue operations.
Hundreds of rescuers with sniffer dogs worked through the night as temperatures dropped to minus 15ºC but the search has now been called off.
Polish Prime Minister Kazimierz Marcinkiewicz has announced a three-day period of national mourning.
Thousands of Polish people attended masses around the country to pray for the dead and the injured.
In Cork, around 1,000 people attended the weekly Polish mass at St Augustine’s Church to say prayers for the dead and the injured.
Bishop of Cork and Ross John Buckley joined Fr Pietr Galus, the chaplain to Cork’s Polish community, in celebrating the mass and Bishop Buckley offered sympathy on behalf of the people of Cork.
Fr Galus said it was very important for the Polish community to come together yesterday and feel solidarity with each other and the Irish community.
“Obviously everybody is shocked because many people died. Everyone has family in Poland, some from this region, and everyone is upset about this.”
Przemyslaw Lesiak, a Polish national living in Cork, said about 15% to 20% of Cork’s Polish community came from the region where the accident happened.
“It was helpful for people to come together today and we are grateful to the bishop for coming here,” he said.
A book of condolences will be opened at the Polish embassy in Dublin on Tuesday.