When people see hope, they turn their backs on darkness, he added.
Instead, he is making way for President-elect Donald Trump, a new leader of the free world who won election by excoriating Obama's democratic worldview. But he added, "We can't look backward for answers".
"The lesson I draw - and I think people can draw a lot of lessons but maybe one that cuts across countries - is we have to deal with issues like inequality", said Obama. He then headed for Germany. Although Clinton was favored to win the election, Trump pulled a surprising upset victory.
Democracy remains the most effective form of government ever devised by man, he said.
Asked for his comments on what the Democratic Party needed to do to improve its prospects for the next elections, he stressed that it had to work on its popular base and cited the need for "new voices and new ideas" to emerge, referring obliquely to the end of the Clinton machine that the November 8 defeat constituted. But in delivering the speech in the birthplace of democracy - and after touring the Acropolis, the iconic hilltop ruins that have become an enduring symbol of Western civilization itself - Obama will also make clear that Trump is not a uniquely American phenomenon.
Obama touted his achievements while in office that he claimed proved the benefits of diplomacy backed by democratic governance, including the nuclear deal with Iran, warming diplomatic relations with Cuba and a landmark climate pact reached in Paris a year ago.
But at the end of a two-day visit to Greece, he reassured his audience that U.S. democracy was bigger than any one person and as long as people maintained their basic faith in democracy, "our future will be OK". He renewed his pledge to ensure a peaceful transition despite his differences with Trump.
There were also reports in the Russian media that Obama is preparing to demand that Greece close its ports to all Russian warships, amid escalating military tensions between the United States and Russia in the war in nearby Syria. "They are right. It is important because if reforms here are to be sustained, people here need to see hope and they need to see progress", he said during the televised address.
Greek Prime Minister Alexis Tsipras won elections previous year on what critics say was a populist platform, though one on the left of the political spectrum.
Greece is now in its seventh year of an extreme debt crisis.
Joining the two leaders were the heads of countries at the centre of numerous European Union's coming challenges.
The speech, which anchors Obama's multi-nation farewell tour to meet more than two dozen foreign leaders, including top US allies in Europe and Asia-Pacific nations, comes against a very different backdrop than the one Obama and his aides had envisioned.
However, his speech to a select audience in the new Athens opera also contained several references to the long-term benefits of democracy, open markets and social inclusiveness.
Obama with Eleni Banou, Ministry of Culture director of Ephorate of Antiquities for Athens, during a tour of the Acropolis. He strolled through the Propylaea, the complex's monumental gateway, and gazed up at the famed Parthenon temple dating to the 5th century B.C. The ancient site will remain closed to the public for the day to accommodate the president's visit.
Obama is the first United States president to visit the country in 17 years. He urged creditors to help Greece dig out of its mountain of debt and called on young people to stay in the country to spur its economic recovery.
"The IMF (International Monetary Fund) has said that debt relief will be crucial to get Greece back to growth".