"No matter how many scars we may carry and how harsh it may be, the nation needs to move ahead", Tsai said in brief remarks at the DPP's headquarters Saturday night in which she also resigned as the party's chairperson.
Observers agreed Tsai's re-election prospects had been severely weakened although some said she still had a chance to run, in the absence of an obvious successor.
And in a highly symbolic but potentially impactful referendum, voters were also asked whether they wish to compete in future global sporting events, including the 2020 Tokyo Olympics, as "Taiwan" instead of "Chinese Taipei" - the name the island is required to use at China's insistence.
Yu Keli, a former director of the Taiwan research center at the Chinese Academy of Social Sciences, noted that the election results will affect future Taiwan-China relationships.
With the conservative vote passing the threshold of 25% of eligible electors, under referendum law the government must take steps to reflect the result.
The DPP lost control of a number of the party's previous strongholds, including the southern city of Kaohsiung.
While the loss of several cities and counties doesn't directly impinge on her ability to govern, it will likely energize the China-friendly KMT as well as embolden opponents within her own party.
According to Taiwanese marriage campaigner Jennifer Lu, American activists from the National Organisation for Marriage were responsible for "instigating the three anti-LGBTQ measures on the ballot". China recently conducted military drills around the island and tried to convince Taiwan's diplomatic allies to abandon it.
They simply want good relations with China and peace and prosperity for Taiwan.
Professor Jin Canrong from Renmin University said election campaigning focused on bread-and-butter issues such as the economy, and one notable trend was greater personalisation in Taiwanese politics, where people voted more for individuals instead of along party lines.
The DPP is traditionally pro-independence and Tsai has refused to acknowledge Beijing's stance that Taiwan is part of "one China", unlike her KMT predecessor Ma Ying-jeou.
The results were nevertheless criticised by political experts, who said they reflected the public's dissatisfaction with President Tsai's performance.
Taiwanese officials had warned that Beijing was seeking to sway voters through the spread of disinformation online similar to how Russian Federation was accused of interfering in USA elections.
Taiwanese media said the political landscape had been dramatically reshaped. The DPP won just six major races.
Economic growth, employment and pension reforms were among key issues in the elections, which drew high turnout from the island's 19 million voters.
"Tsai has made a liberal, progressive society a big part of her appeals to the rest of the world to support Taiwan in juxtaposition to an increasingly repressive China". "One way or another it has to go back to the court".
Chiang Kai-shek's Nationalists rebased their government to Taiwan in 1949 amid the civil war with Mao Zedong's Communists.
They backed the definition of marriage as the union of a man and woman.
Beijing was opposed to the proposal and the International Olympic Committee had warned Taiwan that its athletes risked being excluded from international competition.
China has already responded.
The results of the referendums weren't expected until Sunday.
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