Armstrong was at the head of a nine-man pack when Christian Vandevelde veered suddenly to the right and fell, taking teammate Roberto Heras down on the rain-soaked road.
The seven remaining riders continued, but their pace dropped off, destroying the American squad's chances of winning the stage between Verdun and Bar-le-Duc in eastern France.
"I saw very professional behavior by the team," said U.S. Postal's sports director, Johan Bruyneel. "They stayed calm. At the end, we saw the team finish very strong. It could have been a lot worse."
Still, the fourth-place finish behind the French team Credit Agricole, left Armstrong 15th in the overall standings after five of 20 stages of the world's premier cycling event.
But the Texan remains the favorite to win the Tour. He can easily regain lost time by doing well in the tough mountain stages that begin on Tuesday.
Friday's sixth stage takes riders on a hilly, 211.5-kilometer stretch from Commercy in the Lorraine region to Strasbourg in neighboring Alsace.
Australian rider Stuart O'Grady kept the leader's yellow jersey for a third consecutive day after the 67-kilometer stage Thursday. O'Grady, who rides for Credit Agricole, has a total time of 20 hours, 54 minutes, 21 seconds.
He leads teammate Jens Voigt of Germany by 26 seconds. Another teammate, American Bobby Julich, is an additional second back. Armstrong is behind by 1:53.
"Today's been a surprise for everyone," O'Grady said after the team-time trial.
His team was the last to take the start in Verdun and crossed the finish line after 1:21:32, 31 seconds faster than the second-place Once group. Festina was third.
"We've got no real pressure on us to keep the jersey," O'Grady said. "You just take it one day at a time."
The stage itinerary took riders down the Sacred Route, a section of highway that was the French army's only supply line during the Battle of Verdun, one of World War I's bloodiest episodes.
The road is now classed as a national monument, and each milestone bears a soldier's helmet dating back to the 1916 clash with German forces.
Vandevelde took a tumble 12 miles from the finish, not long after a persistent drizzle turned into a downpour.
U.S. Postal was among the fastest teams when the accident happened, but slowed down for several minutes until Vandevelde and Heras caught up.