The world number 113 was giving away 42 rankings places against her Czech opponent but she more than held her own for the first two sets.
However, Zahlavova Strycov rattled off five consecutive games in the deciding set to seal victory.
The Briton won the first set 6-2 but the second was a completely different affair.
The seventh game was hard fought with Robson eventually prevailing on serve but after her opponent held, it was the Czech who broke for 5-4.
Robson then immediately broke back for 5-5 and looked odds-on for 6-5 but her Czech opponent broke before holding to level up the match and take it into a deciding set.
Robson held but her opponent won the next five games for a 5-1 lead and although the 18-year-old eventually held for 5-2, it was merely delaying the inevitable as Zahlavova Strycov wrapped up victory.