The Indian Davis Cup team was relegated to the World Group II for the first time since the new format was launched in 2019 after losing the playoff tie 2-3 to Denmark on Saturday.
Denmark were single-handedly carried by Holger Rune as the world number nine won three matches for the hosts.
The tie levelled at 1-1 after Friday's matches, India needed to win the doubles but the pair of Yuki Bhambri and Rohan Bopanna lost 2-6, 4-6 in 65 minutes to the home team combination of Rune and Johannes Inglidsen.
India now had to win both the reverse singles to stay in World Group I. Nagal put a brave fight before losing his match 5-7, 3-6 in one hour and 37 minutes in the first reverse singles. The defeat gave Denmark an unassailable 1-3 lead and pushed India to World Group II.
Prajnesh Gunneswaran then took court in the final match of the tie against Elmer Moeller and won 6-4, 7-6 (1) in one hour and 39 minutes.
Earlier on Friday, Nagal had erased a one-set deficit to pip August Holmgren 4-6, 6-3, 6-4 in two hours and 27 minutes to make it 1-1 after Bhambri lost the opening singles match 2-6, 2-6 to the rising teen sensation Rune.
Bhambri had earlier announced that he quit singles and will concentrate playing only doubles on tour.