Serifovic's sombre performance was in stark contrast to the Ukraine's techno-dance entry "Dancing Lasha Tumbai which, performed by drag queen Verka Serduchka, came second with 235 points.
"Serbia had a great song, we really showed Europe what we can do. It was the best song, and she is one of the best singers anywhere," said Aleksandar Miscevic, a Serbian airline steward.
This year's Eurovision Song Contest was held in Helsinki, the Finnish capital, after the country won the competition last year with a song performed by masked rockers Lordi.
Nearly 25,000 fans watched the show on giant screens in Helsinki's central square. Ireland, which has won seven times, came last this year with five points, while the UK and France jointly finished second last with 19 points.
The Eurovision Song Contest, which helped to launch the careers of ABBA and Celine Dion and is the flagship of the European Broadcasting Union's light entertainment programming, was a black-tie event throughout the 1950s.
But in recent years the contest has lost a certain amount of its stature in Western Europe, although it has drawn increasing interest from viewers in Eastern Europe.
All countries in this year's contest avoided the dreaded "nul points".