According to the election commission, just under 55% of those eligible to vote did so - a 10-percentage-point fall from the last elections.
"We don't have all the final numbers but we would have liked them to be higher," said Robert Beecroft of the pan-European Organisation for Security and Co-operation in Europe.
"There are a lot of people who didn't vote. Personally, I would have liked to have seen more young people out and voting."
The BBC's Nick Hawton in Sarajevo said there has been concern for some time that disillusionment among voters would lead to a low turnout and those fears appear to have been realised.
The poll has been seen a crucial choice for the people of the recently war-torn country from continuing with reform or turning back to the ethnic divides of the past.
Some observers believe a low turnout could benefit the nationalist parties, who in the past have proved more able to get their vote out on election day.
Counting underway
Voting had taken place throughout Saturday without incident in these elections, which were the first run by Bosnian authorities since the 1992-95 war.
Results are expected from Sunday evening onwards, but with as many as 50,000 votes to count from Bosnians living abroad, the final results will not be announced for several days.
More than two million people were entitled to vote to decide who controls the parliaments, presidencies and prime ministerships of Bosnia's complex post-war political system.
The European Union and United States urged a pro-reform vote, fearing that economic discontent could push people back into the arms of the nationalists who led the country to war 10 years ago, or turn them off from voting at all.
"I'm not sure if any of the candidates can offer change. I am afraid we are only choosing between the devil and the deep blue sea," said Rasid Cindra, an unemployed factory worker in Sarajevo.
"I only know that we must vote for change as electing those who led us into war would mean a disaster," said retired hairdresser Ljerka Samardzic.
In the 1995 peace accords, Bosnia was divided into two autonomous entities - the Muslim-Croat federation and the Bosnian Serb republic, Republika Srpska - but maintained an overall, multi-ethnic administration.
Saturday's vote was to elect:
For the first time, those elected will serve a four-year, rather than a two-year, term.
Serb nationalists
Opinion polls indicated that nationalist Serb parties were likely to perform well in the Republika Srpska.
"When Muslims stop showing their hatred toward us I will consider voting for some parties with proper reform programmes," said Miladin, who was voting for the nationalist SDS party - set up by the wartime leader Radovan Karadzic, currently on the run from the international war crimes tribunal.
The SDS's Mirko Sarovic, who is aiming for the Bosnian Serb seat on the presidency, provoked outrage recently by calling Mr Karadzic a "symbol of freedom" for Bosnian Serbs.
Moderates' hopes
In the Muslim-Croat federation, moderates were better placed for success.
The Bosnian Croats' most popular party, the HDZ, flirted with nationalism after the last elections - launching an abortive attempt to launch a new entity, separate from the Bosnian Muslims.
But moderates are now seen to rule the roost there and the leading candidate for their presidential post is Dragan Covic, who served as a minister in the Muslim-Croat federation government.
Charismatic former Prime Minster Haris Silajdzic is hoping for the Bosnian Muslim seat.
He annoys Croats and Serbs by calling for the unification of Bosnia, though he helped broker the deal which divided it.
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