Switzerland's Fabian Cancellara of the Saxo Bank team narrowly kept the yellow jersey lead following the fourth stage, a 24.2-mile ride in and around Montpellier.
Astana needed to beat Saxo Bank by more than 40 seconds for Armstrong to take the yellow jersey. The seven-time champion started the stage in third place, and Astana exactly matched that 40-second deficit. Cancellara's team finished third.
"That's Swiss timing," Cancellara said, laughing. "Time is on my side."
Armstrong credited his teammates but acknowledged he had hoped to move in front.
"This is a little bit of a disappointment," he said. "That's cycling."
The 37-year-old Texan said the many tight turns along the course made for "tricky" riding. Three crashes marred the start of the stage, including one involving Giro d'Italia winner Denis Menchov.
The U.S. team Garmin was second in the stage, 18 seconds after Astana, despite only five of the nine riders being able to keep up the pace.
Armstrong and Cancellara share an overall time of 10 hours, 38 minutes, 7 seconds, although the Swiss rider is technically considered a second ahead.
Three Astana riders follow in the overall standings. Alberto Contador of Spain, the 2007 Tour winner, is 19 seconds behind. Andreas Kloden of Germany is 23 seconds back, and Levi Leipheimer of the United States trails by 31 seconds.
Next up is Stage 5, a 122-mile ride along the Mediterranean from Le Cap d'Agde to Perpignan. The Tour ends July 26 in Paris.