As footage of their best moments played out on a video wall behind them, the players sang and danced along with the flag-waving crowd.
"We're extremely happy to bring this trophy to Croatia and to show everyone that we are the best," Cilic said from the stage as he held up the prize.
Croatia's 3-1 defeat of France over the weekend was the second time it has won the trophy, after beating Slovakia in 2005.
It was also Croatia's second major sporting clash with France this year - the first was Croatia's 4-2 defeat in the World Cup soccer final in Moscow in July.
"We are proud of our guys. They struck back after the defeat of our soccer team," one of the revellers in Zagreb said. (Reporting by Igor Ilic Editing by Andrew Heavens)
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