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The GB1 crew were lying fourth after two runs, 0.02 seconds off bronze, but they rolled over on corner nine.
Lamin Deen, Ben Simons, Bruce Tasker and Joel Fearon emerged unscathed but they missed out on a fourth run for the top 20 sleds.
"It's hugely disappointing," said performance director Gary Anderson.
"But they are strong characters and I have no doubt they will bounce back from this and be better for it.
"They have shown they are truly world-class and we need to make sure we remember that as we build towards the next Winter Olympics in two years' time.
"They were on course to be within a tenth of a second off the leaders at the end of run three and would have been ahead of the eventual gold medallists going into the final run."
GB's other crew, led by John Jackson, finished in 11th place, while Oskars Melbardis of Latvia took his team to gold ahead of Germany and Switzerland.
Great Britain's hopes of winning a first four-man bobsleigh medal in 77 years ended with a crash at the World Championships in Igls, Austria.