The Czech slumped to a 6-4 6-4 defeat against world number 75 Darcis.
Berdych, the sixth seed here, lost his opener on Centre Court at the Wimbledon Championships to Ernests Gulbis.
Berdych reached the final of Wimbledon two years ago, losing to Rafael Nadal, and had been expected to provide a challenge to Host Nation favourite Andy Murray in the quarter-finals here.
Seventh seed Janko Tipsarevic had no such problems against Argentina's David Nalbandian, the Serb coming through 6-3 6-4 to set up a meeting with Germany's Philipp Petzschner.
Darcis next faces Santiago Giraldo of Colombia.
The 28-year-old said: 'It was amazing. When you are young, you watch the Wimbledon final, you watch all the brilliant matches here, and you say, "Maybe it will be my turn one day".
'It was amazing to step on the court, to see all the crowd. Of course, it was different. It was the Olympics.
'You play tennis to play those matches, to play on those courts. Today was one of the best moments in my life.'