UTN came fifth in the election with 36 MPs, behind Move Forward with 152, Pheu Thai (141), Bhumjaithai (70) and Palang Pracharath (40).
Prayut said he congratulated the elected MPs during the UTN's meeting at headquarters in Bangkok's Phaya Thai district and asked them to continue with party activities.
He added that the party will study the general election results to prepare for future polls.
He denied having said that the forming of the Move Forward government depended on the future.
It is currently in the process of being formed and we must respect that, he said, adding that he only wants to see Thailand enjoy peace and order.
Prayut also vowed to maintain UTN's philosophy towards the nation, religion and the monarchy, adding that people had already forgotten the military coup nine years ago.
A coalition of eight parties led by Move Forward on Monday signed a memorandum of understanding (MoU) as a prelude to setting up the next government.
They are Pheu Thai, Thai Sang Thai, Prachachart, Seree Ruam Thai, Pheu Thai Ruam Palang, Fair Party, and Plung Sungkom Mai Party.
The date and time chosen for the signing of this MoU was of great symbolic significance, as it marked the 9th anniversary of the 2014 military coup. Thailand's 13th coup toppled the elected government of Yingluck Shinawatra and brought Prayut to power as the prime minister.
Even though the coalition has 313 MP seats in total, it is still not enough to set up the government as the 2017 Constitution stipulates that the candidate for prime minister must obtain more than 376 votes from MPs and the Senate.