Opponents want the results invalidated.
The elections, coming in the midst of more than two months of vigorous and sometimes violent protests against the government and boycotted by the main Democrat Party, ended Sunday with voting in 89 percent of the country's 375 constituencies, the Bangkok Nation reported.
It will be weeks before the results of the elections are known.
Speaking to the BBC, Yingluck said the elections showed the people want to continue with the democratic process.
She said she was satisfied the elections could be completed without violence.
Anti-government forces expressed determination to continue with their protests and Democrat Party officials said they were collecting evidence to seek a Constitution Court ruling to invalidate the elections, indicating the possibility they could end up being declared void, the Nation reported.
At least 10 people have died and several hundred injured since the protests began in November.
Democrat Party deputy leader Ong-art Klampaiboon called on the Yingluck government to revoke a state of emergency imposed in Bangkok and neighboring areas before the elections. He said the government had insisted on the elections because it wants to stay in power as long as possible.
The Nation said there was unusually low voter turnout in many provinces, including parts of the north and northeast where Yingluck's ruling Pheu Thai Party has remained popular.
There were reports of a large number of "no votes" in some provinces, meaning those voters checked the box for "none of the above," the Nation said.
The Nation quoted one official as saying an estimated 12 million people, or 25 percent of all 48.7 million eligible voters, had failed to cast ballots.
Protest leader Suthep Thaugsuban said it was the "first time to have so many eligible voters boycotting an election," the Nation reported.
The protesters want to oust Yingluck and end the influence of her older brother, former Prime Minister Thaksin Shinawatra, who has lived in exile since being removed from power following a coup in 2006.
Protesters, who are seeking sweeping reforms in the country, want a "people's council" to oversee the elections.
The Election Commission said holding new elections in the disrupted provinces could likely take as long as six months.