Speaking on television, Ms Yingluck said the rallies could hurt the economy and talks were needed.
Her government is facing the biggest demonstrations to hit Thailand since the violence of 2010.
UN chief Ban Ki-moon has voiced concern over the tensions and called for all sides to exercise restraint.
Protests began in Bangkok on Sunday. Since then, demonstrators calling on the government to step down have marched on ministries and government bodies in an attempt to shut them down.
In the latest disruption, the protesters cut the electricity supply to the national police headquarters.
The demonstrators, who are led by a former opposition party lawmaker, say Ms Yingluck’s government is controlled by her brother – the ousted former leader Thaksin Shinawatra.
Ms Yingluck has invoked special powers allowing curfews and road closures, and police have also ordered the arrest of the protest leader – but so far no move has been made to detain him.
The protests have been largely peaceful and correspondents have described the mood of the rallies as friendly.
On Wednesday, hundreds of protesters surrounded Thailand’s top crime-fighting agency, forcing its evacuation.
The UN leader Ban Ki-moon has urged all sides to “refrain from the use of violence and to show full respect for the rule of law and human rights”.
The no-confidence motion was brought by the opposition Democrat Party, but Ms Yingluck’s Pheu Thai party dominate the chamber and voted it down by 297 votes to 134 votes.
Speaking on television shortly afterwards, Ms Yingluck said the two sides should negotiate.
“The government doesn’t want to enter into any political games because we believe it will cause the economy to deteriorate,” she said.
It is not clear what the protesters will do next, the BBC’s Jonathan Head in Bangkok reports.
So far they have succeeded only in disrupting the business of government for a few days, and the authorities have been careful not to risk violence by confronting them, our correspondent adds.
Earlier, Thai Education Minister Chaturon Chaiseng told our correspondent that the Pheu Thai party would have to find a balance and demonstrate it was not controlled by Mr Thaksin.
“They will need to make it clear that whoever is going to be prime minister can show that they have independence and can make a decision on their own,” he said.
“The fact that some people do not believe in the government or the coalition parties anymore doesn’t mean they can either overthrow the government or change the system,” he added.
Mr Chaturon said that he did not believe a coup was imminent, although he added that “in my experience a coup can take place any time”.
Mr Thaksin was ousted in a military coup in 2006 that left the country bitterly divided.
In 2010, thousands of “red-shirt” Thaksin supporters occupied key parts of the capital. More than 90 people, mostly civilian protesters, died over the course of the two-month sit-in.
Ms Yingluck and the Pheu Thai Party were subsequently voted into office, and Thailand’s political landscape has remained largely stable since then.
But a now-shelved political amnesty bill that critics said would have facilitated the return of Mr Thaksin without having to serve a jail term reignited simmering political tensions.