Konta powered into a 4-1 lead in the first set but Strycova never panicked and used her superior craft to turn the match in her favour in front of a deflated Centre Court crowd.
After playing a superb tiebreak to take the first set the 33-year-old Strycova took complete charge of the match as Konta self-destructed with a flurry of wild errors.
Konta had raised hopes of a first British women's singles champion at Wimbledon since 1977 with a strong run to the last eight, but she was well-beaten in the end.
World number 54 Strycova will face seven-time champion Serena Williams in her first Grand Slam semi-final.