"We are having some problems, but we are very positive," he said. "We are an amazing nation."
The director said movies could help Latin America "learn from the mistakes of the past".
A jury led by Mexican director Alfonso Cuaron chose winners from among 21 movies competing at the 72nd annual festival - an edition where war, crime and other woes of the world dominated on-screen.
Audiences saw African child soldiers drafted into a brutal civil war in Cary Fukunaga's Beasts of No Nation, Afghan civilians caught between the Taliban and Danish troops in Tobias Lindholm's A War and Turkish brothers trapped in escalating political violence in Emin Alper's Frenzy.
Alper's film won a special jury prize at the festival.
Director Jonathan Demme, jury president for the festival's Horizons competition for emerging talents, said many of the films gave "horrifying glimpses of how hard it is to stay alive in the world today".
The top Horizons prize went to US director Jake Mahaffy's drama about a faith healing gone wrong, Free in Deed.
Several hotly tipped European contenders were overlooked for prizes, including Italian film-maker Marco Bellocchio's lush vampire fable Blood of My Blood and Russian director Aleksandr Sokurov's art-history meditation Francofonia.
Cuaron said he was very happy that a Latin American movie had won the Golden Lion for the first time. But he said it was a coincidence that it had happened when a Mexican headed the jury.
Italy's Valeria Golino took the best-actress trophy for playing a put-upon Neapolitan woman in Giuseppe Gaudino's experimental family drama For Your Love.
France's Fabrice Luchini was named best actor for his role as a judge trying to rekindle romance while presiding over a murder trial in Christian Vincent's L'Hermine.
The jury also gave the best young actor prize to 14-year-old Abraham Attah, the Ghanaian star of Beasts of No Nation. American actor-director Brady Corbet won the first-feature prize for The Childhood of a Leader, an ambitious exploration of the roots of dictatorship.
The film festival also identified some early potential Oscar contenders, including Johnny Depp for his performance as gangster Whitey Bulger in Black Mass, and Eddie Redmayne as a transgender artist in The Danish Girl.