The 30-year-old welterweight, who struggled for years after losing to American Floyd Mayweather in the quarter-finals of the 1996 Olympics in Atlanta, outclassed the Greek fighter in a first-round bout.
Vocal support from the fans at the Peristeri hall could not help Kotakos, who was trailing by 28 points when the referee stopped the contest in the third round.
"It was very easy but you should not under-estimate anybody in this sport," said Aragon, who has fought more than 400 bouts in a career spanning over a decade.
"We always keep our feet on the ground and that's one of the reasons for Cuba's domination," he added.
Aragon, who failed to qualify for the Sydney Games but made it back to the top with world championship triumphs in 2001 and 2003,
Martirosyan, one of the hopes of an American team desperate for a title after leaving Sydney without one, easily survived the opening round by outpointing Algeria's Benamar Meskine.
"I felt full of confidence," said Martirosyan. "My coaches had told me to be comfortable, to box naturally and not to rush. That really helped me."
The 18-year-old Martirosyan has talent but is still learning and should not trouble Aragon, the man most likely to stop Russian Oleg Saitov in his quest for a rare Olympic treble.
Saitov, in action later on Sunday, is trying to become the fourth boxer to win three Olympic titles and the third to do it in the same weight class after Cuban all-time greats Teofilo Stevenson and Felix Savon, both heavyweights.