The 22-year-old Dane missed out on a place in the semi-finals when she lost 3-6, 5-7 to Russian outsider Anna Kalinskaya on Saturday night.
As the fourth seed in the tournament, Tauson went into the game as favorite against Kalinskaya, who is four years her senior and ranked No 48 in the world while Tauson is ranked 19th.
Tauson quickly fell behind in the first set, where she was broken three times in her own serve.
In the second set, Tauson still couldn't get her game going against the strong Kalinskaya, and the Dane trailed 3-5 after a new Russian service breakthrough.
In the next game, the Dane broke to 4-5, and a little later she also equalized to 5-5 giving her hope of a possible comeback, but it was quickly extinguished.
On the other side of the net, Kalinskaya got hold of herself and the Russian won the next two games to close out the match.