While Moscow was keen to get a dependable mayor to prepare for the games, the vote had also been touted as "good for democracy" by Medvedev and was thus seen as a test of the president's credentials.
Ilya Yashin, the campaign manager for Nemtsov, a former deputy prime minister who has now become an outspoken Kremlin critic, said that Nemtsov would be protesting against the results.
Yashin said high levels of early voting, in which voters cast ballots in advance of Sunday's poll, were evidence of rampant bribery and voter harassment.
While between one and five per cent of votes are usually cast early in Russian elections, in Sochi nearly 11 per cent of registered voters cast their ballots ahead of the polling day on Sunday.
"There would have been a second round if it were not for the ballot-stuffing," Yashin said.
Yury Dzagania, the Communist party candidate, echoed those charges.
Nemtsov garnered only 13.5 per cent while the Communist candidate collected about seven per cent of votes, officials said.
Seven candidates were earlier excluded from the race due to alleged registration errors, including a ballet dancer and Alexander Lebedev, an ex-KGB agent who is now a billionaire and owns Britain's Evening Standard newspaper.
Medvedev had portrayed the Sochi vote as "a full-scale political battle" in an interview with Novaya Gazeta, an opposition newspaper, last week.
In 2007, Russia won the right to host the 2014 Winter Olympics in Sochi, with strong support from Putin, who was president at the time and is personally supervising the preparations.
Moscow has earmarked about $12bn to upgrade the town's Soviet-era infrastructure and build new facilities from scratch in preparation for the Olympics.