The president said her administration is moving in the right direction and has launched several major reforms over the past two years since she came into office, but she admitted that Taiwanese people are clearly setting an even higher standard for the party.
There was no immediate reaction from Beijing to the poll results, where state media simply noted Ms Tsai's resignation as party chairwoman "to take responsibility for the party's performance in Taiwan's local elections".
The DPP lost control of a number of the party's previous strongholds, including the southern city of Kaohsiung.
In a statement, Marriage Equality Coalition Taiwan said it was "deeply saddened" by the referendum results and "all progressive causes have suffered the backlash of conservative forces". Beijing has been ratcheting up pressure on the island it claims as its own territory by poaching its diplomatic partners and barring its representatives from worldwide gatherings, while staging threatening military exercises and limiting the numbers of Chinese tourists visiting Taiwan.
The state-run China Daily said Taiwan's people are unhappy the government has not pulled the island out of quasi-economic stagnation and that its policies "have ignored the interests of many groups". The government has said it will still press on with new laws but they may now be weaker.
As for public sentiment regarding Taiwan's relations with China, Taiwanese online media Up Media, in an opinion article published on November 25, pointed out that neither DPP nor KMT candidates mentioned at length their positions with regard to their China policy, indicating that there is a consensus among the general Taiwanese public that unification with China isn't an option.More news: Nittany Lions No. 12 In Latest College Football Playoff Rankings
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 had accused mainland China of engaging in "political bullying" and "fake news" in the run-up to the elections in a bid to sway voters.
The KMT won 15 of 22 mayoral and county magistrates seats, up from just six. Although she resigned as head of the DPP after the election loss, Tsai faces no obvious challengers from within who might stop her from seeking a second term as president.
Another factor cited was the Nationalists' Han Kuo-yu, who ended 20 years of DPP rule in Kaohsiung by soundly defeating his DPP rival, and seemed to galvanize opposition to the status quo under Tsai.
"We hope the two sides will soon go back to a peaceful and stable trend in relations", he said. They ruled under martial law until the late 1980s, when the native Taiwanese population began to take political office, mostly through the DPP.
Seven million voters backed a definition of marriage as the union of one man and one woman.
The vote against changing the name used in worldwide sporting events to Taiwan was seen as a test of support for independence. Earlier this year, it forced a vote at the Asian Olympic Committee to withdraw the right of Taichung in central Taiwan to host a youth competition scheduled for next year.