Saina became the first Indian woman to reach the semifinals of the prestigious tournament but her journey was cut short by Rasmussen of Denmark, who beat her 21-19 21-17 in a 37-minute battle.
Down 1-5 in the first game, Saina picked up four straight points to make it 5-5 and then moved neck and neck till 19-19 but Rusmessen had the last laugh as she sealed the game with two straight points.
In the second game, the world number seven Indian had raced to narrow lead of 3-1 but the Dane soon surged ahead at 9-4 and held the fort as Saina's game crumbled.
Earlier, the Hyderabadi had beaten German Juliane 21-8, 21-14 in just 27 minutes to reach the semi-final at the National Indoor Arena in Birmingham.
Saina had also beaten Judith Meulendijks of the Netherlands and Korean Seung Hee Bae in the first two rounds of the tournament.