The bodies of the men and women were found inside a sealed container near London in October 2019, after they suffocated in sweltering temperatures.
Truck driver Eamonn Harrison, 24, from Northern Ireland, and Romanian national Gheorghe Nica, 43, were found guilty of 39 counts of manslaughter, as well as people smuggling, by a London court on Monday.
They are expected to be sentenced early in January and could face a maximum sentence of life imprisonment.
Nguyen Dinh Gia, father of victim Nguyen Dinh Luong, 20, expressed sympathy for the men.
"I think they only did it because they wanted to make ends meet. I don't think it's appropriate to give them a harsh (punishment like) a life sentence," he told AFP from a small village in Vietnam's Ha Tinh province.
"I feel sorry for them."
Le Minh Tuan, who lost his 30-year-old son Le Van Ha, hailed the court verdict.
"I think the decision of the U.K. court that convicted two men of manslaughter is right," he told AFP from his village in Nghe An province.
"If they had given the migrants inside some air, those people wouldn't have died. In this case, I think the driver knew, but he kept running the truck and did not give the air to people inside."
The bodies were discovered at the southeastern English port of Purfleet after being sealed inside the container for at least 12 hours.
A forensic expert calculated it would have taken about nine hours for the air to turn toxic in the trailer.
The victims were aged between 15 and 44.
Prosecutors have said the trapped Vietnamese were unable to get a phone signal inside the container.
Mobile phones recovered from the bodies of the 39 victims showed they had tried to raise the alarm and left messages for their families as they ran out of air.
The case highlighted the vast and unscrupulous people trafficking networks spanning the globe.
Many of the victims had come from poor parts of Vietnam and were plunged into thousands of dollars of debt to smugglers to pay for the dangerous journeys.
Monday's convictions brought the total number found guilty in connection with the case in the U.K. to eight.
Prosecutors at the trial said the people smuggling ring had been motivated by greed, and are considering charges against a further three people.