Former prime minister Yingluck Shinawatra has bemoaned the country "moving backwards" by accepting the draft charter in Sunday's referendum.
In her Facebook, the ex-premier said she was not surprised more people favoured the draft charter than those who rejected it because people were not allowed to freely express their opinions or debate the draft.
She said she regretted the country is now moving backwards having adopted a draft charter which is undemocratic.
Democrat Party leader Abhisit Vejjajiva, meanwhile, said the referendum outcome showed most voters wanted the country to move forward and they were satisfied with the state of peace and security.
He said the parties should also review their roles. Critics have said the referendum result may indicate the people's frustration with the politicians they hold responsible for conflicts and social division.
Mr Abhisit was optimistic the National Council for Peace and Order (NCPO) would be able to implement its roadmap for restoring democracy as planned as long as it pays attention to the minority voice.
The country should learn from past political crises which stemmed mainly from the majority voice, which was running the country, refusing to listen to the minority, he said.
He dismissed speculation the referendum result showed a decline in his party's popularity in the South, its political stronghold. Overwhelming votes were cast in most southern provinces in favour of the draft despite Mr Abhisit's stance before the referendum that he would not accept the draft charter.
The Democrat leader insisted the vote result would not shatter the party because as party leader he had expressed his stance against the draft charter.
The results of the referendum bore similarities to the 2007 one where the political party leading the "Vote No" campaign went on to win the subsequent general election, he said, referring to the Pheu Thai Party.
Akanat Promphan, spokesman of the Muan Maha Prachachon for Reforms Foundation (MMPRF), however, said he thought voters had broken free from the influence of the two main parties, the Democrats and Pheu Thai, in Sunday's vote.
The proof was the fact the majority voted Yes despite a shared clear stance announced by Democrat and Pheu Thai heavywieghts that they would vote against the draft charter, said Mr Akanat.
He thought the winning Yes votes reflected a combination of the popularity of Prime Minister Prayut Chan-o-cha, who had pledged to vote Yes a few days before the referendum, and people's hope for a swift suppression of corruption that is the highlight in this draft charter, said Mr Akanat.
The result was not a victory for any party or group but of the people whose opinions have not been heard through conventional media before, and who voted in favour of the draft charter, said Thaworn Senneam, a former People's Democratic Reform Committee leader and a former Democrat MP for Songkhla.
Somsak Prisananathakul, a key figure in the Chartthaipattana Party, meanwhile, called on the NCPO to relax its ban on political gatherings so political parties can call a meeting of their executives. They have been banned from meetings since May 22, 2015.
Noppadon Pattama, legal adviser to ousted prime minister Thaksin Shinawatra, echoed Mr Somsak's call.