Pham Minh Tuan played in the fourth singles match and was defeated 6-3, 4-6, 7-6 by world ranked No 904 Pruchya Isarow.
Later on, 17-year-old Nguyen Dac Tien was also defeated, 3-6, 0-6, by Kittiphong Wachiramanowong.
Earlier, Vietnam lost 0-3 to Thailand during the first two days in two singles and one doubles matches.
The victories helped Thailand move to the third round to play either Chinese Taipei or the Philippines in the final, which will then determine which team moves along to Group I.
Vietnam will continue to play in Group II next season.