A few days after turning 20, the left-hander struggled to get to grips with her opponent's game as she lost in the first round for the third successive year.
Last month Vondrousova fell just short of becoming the first Czech woman to win the French Open for 38 years when she lost to Australia's Ash Barty in the Roland Garros final.
But she only picked up her first Tour grasscourt win last week in Eastbourne and her inexperience on the surface told.
Vondrousova said she was also bothered by a painful hand.
"I think she (Brengle) is a great player for grass, so I think she played a great match," the Czech told reporters. "And I'm having some troubles with my hand, so that was also the key for the match, because she played to my forehand and it hurt.
"I think she knew that and she played it clever."
Latvian Jelena Ostapenko, who went one better than Vondrousova and won the 2017 French Open, also made an early exit, losing to tricky Taiwanese 28th seed Su-Wei Hsieh 6-2 6-2.
(Reporting by Martyn Herman; Editing by Alison Williams and Ken Ferris)
