His clan was already known as Honduras's most successful football dynasty but last week they became the first to have a trio of siblings in a World Cup squad when coach Reinaldo Rueda called up a third member of the family.
Jerry Palacios has joined younger brothers Wilson and Jhony in South Africa, where the Central American underdogs are competing at the finals for the first time since 1982 after scraping through the qualifiers.
"It's an extraordinary thing for this family," Eulogio, 63, told Reuters in a telephone interview from La Ceiba, the family's home city on Honduras's palm-fringed Caribbean coast.
"Now they have to do something extraordinary for the country," added Eulogio, a former player who still trains local youngsters.
"Me and my brothers played professional football and the one who didn't play was a professional referee," he said. "In our family, it's something natural."
Jerry's last-minute inclusion in the 23-man squad because of an injury to Julio Cesar de Leon is especially poignant for the family because it comes a little over a year after the body of kidnapped younger brother Edwin was discovered.
Eulogio said his sons would think of Edwin more than ever at the tournament, saying: "They know he is watching over them."
The Catrachos lost their Group H opener 1-0 to Chile but Eulogio is optimistic ahead of Monday's game against European champions Spain, who lost their first game to Switzerland by the same score, at Johannesburg's Ellis Park.
"We're going to get a draw. A draw still helps us because we'll still have the possibility of beating Switzerland," Eulogio said, adding he been giving his sons advice over the telephone.
"The three of them are staying together so we started chatting and I was giving them tips on how to behave, telling them to make sure they do things right because the whole world and the whole of Honduras is watching," he said.
"I feel like the proudest father on earth."
