In her first WTA Tour semi-final, the 18-year-old Robson took the first set after breaking her eight-seeded opponent twice.
But, having broken the Czech back to save the second set, Robson floundered on her second serve and was broken at the last to bring it level.
An early break in the deciding set put Zahlavova Strycova in charge, and Robson cracked under the pressure, a total of 18 double faults highlighting what was a step too far for the young Briton.
The epic match lasted over two-and-a-half hours but the good news for Robson is that she will now move into the world top 100, meaning she is likely to earn her place at the US Open by right.
Zahlavova Strycova will face top seed and French Open finalist Sara Errani in Sunday’s final after the Italian favourite beat Romanian Irina-Camelia Begu 6-4 6-1.