Tomas, his brother Francisco - a halfback who had a couple of games for Argentina in 2009 - and Alejandro were in the 70,000 crowd when a stray clearing kick allowed the All Blacks to strike.
As the boys dealt with the frustrating defeat, Alejandro recounted his own experience of being close but yet so far against the All Blacks.
Cubelli, who played for the Brumbies this year, is the odd man out in the current Pumas squad as the only overseas-based player.
After the Jaguares were admitted to the Super Rugby competition, Argentina followed New Zealand's lead by stipulating that test candidates must play at home although they give dispensations to any Super Rugby player.
Cubelli wanted to challenge himself under different conditions and coaching, and hopes a few of his countrymen follow his lead to develop their game. He says the eligibility rule works because the Pumas are all at the same stage of the season, and with almost all of the squad training together at the Jaguares they can be more "ambitious" on attack.
Cubelli will face his test mates next season when the Brumbies play the Jaguares for the first time, meaning divided loyalties for his dad.
"I believe the game is in Buenos Aires - he will support his son, he must," laughs Cubelli, who will play off the bench in Saturday night's test in Hamilton.
More importantly, Cubelli would love to deliver a win over the All Blacks for his dad whose own father started the family's rugby tradition while working for an English school in Buenos Aires. That impressive heritage includes Alejandro managing the 2011 World Cup squad in New Zealand.
A strong 2015 World Cup showing, where they attacked with aplomb, and two recent wins against South Africa - including last week - suggest the Pumas are firming as members of rugby's top echelon.
"We were expecting to win (in Argentina last week) and we made it happen. We have been learning our lessons," said the 27-year-old Cubelli, who is studying to be an architect.
On the chances of victory over the All Blacks, Cubelli says: "I think we can play a good game this week but whether we can win depends on what the All Blacks bring to the game.
"Sometimes in the past Argentina has been close to big victories and lost in the last 10 minutes. Soccer fans turn the TV on and say that we are losers again. But we have learned our lessons...beating South Africa has made people think differently.
"We work to win very game. We will try to go to the field not expecting anything against the All Blacks, but just give our best and keep working. One time, it will happen."
