Greene was forced to wait to try to claim a fastest loser spot after finishing fourth in his semi-final with a time of 48.19s.
The Welshman told BBC Sport: "I just can't believe it. Coming down the home straight I couldn't catch them up. I should be better than that.
"I'm devastated. I thought I went off at a decent pace. I just didn't feel like myself and I'm shocked."
Greene trailed behind rivals Felix Sanchez and Jehue Gordon in a disappointing performance, and must wait for the results of the two other semi-finals to discover his fate.