Soccer fans of a certain age will always remember Falcao at the World Cup in 1982 and his starring role alongside Zico, Socrates and Cerezo in one of the greatest Brazil sides of all time.
Their heartbreaking 3-2 defeat by Italy in the second group stage that cost them a semi-final spot was unforgettable and the tournament etched Falcao's name in the history books.
But when he looks back on the great moments of his career, another less heralded occasion still warms his heart.
The 1972 Munich Olympics was a disappointment for Brazil's players but losses to Denmark and Iran, sandwiching a draw against Hungary, tell only half the story.
The Olympics, Falcao told Reuters, was something special.
"It was a unique moment," he said in a telephone interview earlier this month just before returning for a third stint as manager of Internacional where he started his playing career.
"The Olympics is grander than the World Cup because you are alongside the greatest athletes of all the world's sports. In football, it's just footballers.
"Even though football usually gets all the headlines the Olympics is unique because of that rubbing of shoulders in the Olympic village.
"Everyone walked about and everyone could see everyone else, we sat together in the cafeteria, we swapped keyrings with other athletes, it really was beautiful."
Falcao need not feel bad about Brazil's awful campaign in Munich since their failure to win a soccer gold is a regular sob story even in the modern era where top professionals compete.
Until 1992, the Olympic soccer tournament was for amateurs and most of the 1972 team were teenagers. Future AS Roma great Falcao, who would win Serie A, two Italian cups and a European Cup runners-up medal, was just 18 years old.
Since professionals under the age of 23 were admitted, Brazil have still struggled. They have been in the tournament 12 times, losing three finals including at London 2012.
The list of players who have tried and failed to win Olympic gold reads like an all-time greatest Brazil team.
As well as Falcao they include Junior (1976), Dunga (1984), Taffarel and Romario (1988), Roberto Carlos and Ronaldo (1996), Lucio and Ronaldinho (2000), Thiago Silva and Marcelo (2008).
The Olympic gold medal is the only international title Brazil have not won and they are desperate to finally break that hoodoo in front of their own fans next month.
They have senior team captain Neymar among their three-over age players and can also count on a host of other big names including Neymar's Barcelona team mate Rafinha, Marquinhos from Paris St-Germain and Felipe Anderson of Lazio.
Santos' Gabriel Barbosa and 19-year old Gabriel Jesus, who have both been linked with Europe's big clubs, will play alongside Neymar up front.
Brazil open their campaign against South Africa in Brasilia, before playing Iraq at the same venue and Denmark in Salvador.
Falcao said the pressure this year will be twice as great in front of a home crowd.
Brazil have shown psychological frailties in recent years, notably in the 7-1 collapse against Germany in the World Cup semi-final in 2014, but the man known as the 'King of Rome' said the key will be making the pressure work in their favour.
"It is the only title we haven't won so the press talk about it every day and that creates a pressure," said Falcao.
"But I think the pressure, if they learn how to work with it, can be positive rather than negative. The advantage is that the Olympic team now are all highly professional, they all play in difficult leagues and they are as good as the others.
"We are one of the favourites, as we always are."