Halep led 5-2 in the final set against Hsieh Su-wei, but duly lost five games in succession to leave Karolina Pliskova as the only top-10 seed remaining in the women's singles.
The French Open champion reached the Wimbledon semi-finals four years ago and made the last eight in 2016 and 2017.
However, after losing to Hsieh, Halep said: "It's always a big challenge to play on a grass court.
"The ball is not bouncing two times in a row the same. It's really tough to stay low, to play every ball, to expect actually nothing because you never know where the ball is bouncing and where is coming.
"I cannot play my best tennis here, but I hope to improve more for the next years, to have a better result in the future."
Halep gave credit to Hsieh, the world number 48 having already come from a set down prior to her dramatic late comeback.
"She deserved to win," added the Romanian. "She played really well. She stayed there for every point. All the credit to her.
"I just believe that I was not very positive on court. The match was very unprofessional for me. But I am too tired, I was too tired, I have pain everywhere.
"I will not find the excuses about this match. She deserved to win, but still I'm sad about myself."
The draw may now be wide open, but Hsieh brushed off suggestions that an unseeded player could triumph.
"I just try to enjoy the tennis and enjoy the city, enjoy the food," said the 32-year-old. "I feel I'm really lucky to be a tennis player, stay here until the second week. I'm very, very grateful and thankful for all this."