As David Millar warmed down on his stationary bike after yesterday's team time trial, reflecting on another missed shot at the Tour de France's yellow jersey, his sister came over to hug him.

"You wanted it too much," said Fran Millar, a media officer at Garmin-Sharp's rivals, Team Sky.

Two days after missing out on yellow by one second at the end of Stage 2, the Scot could not help Garmin-Sharp, the pre-stage favourites, to win the 25km collective effort against the clock to claim the jersey he wore 13 years ago when he won the Tour prologue in Poitiers.

"We did our best. It was not a good day, that lost us some time," Millar said, sweat still dripping down his chest. "We would have been better on a more technical, up-and-down course."

Garmin-Sharp were four seconds behind the early pacesetters, Omega Pharma-QuickStep, at the 13km time check but ran out of gas, finishing in sixth place, 17 seconds behind the stage winners, Orica-GreenEdge.

"Yes, I'm very disappointed," said Millar, who won a stage in last year's Tour, adding with a grin: "Life's not fair."

On Sunday, Millar came tanta-lisingly close to taking the yellow jersey but Jan Bakelants' win by a single second meant he had to wait for yesterday's time trial to have another go.

"It was really hard not to have it in my head beforehand," said Millar. "You try to think about the job to do rather than the reward, but it's such a big thing and I came so close on Sunday that it was unavoidable I would be thinking about it.

"We know we are one of the strongest teams, but everyone at the Tour de France is incredibly strong. It's disappointing, but there's still two weeks of racing to go."

There is still a chance for Millar to jump into a breakaway in today's undulating stage from Cagnes-sur-Mer to Marseille, but he said that Garmin-Sharp were aiming at the overall standings. "I've used all my opportunities; I'm here for the team," he said. "It's a team that is primarily here for GC [general classification]."

Millar said he would spend the remaining weeks pursuing a very different agenda as he tries to help his team-mates – Ryder Hesjedal, Dan Martin, Andrew Talansky and Christian Vandevelde – in the general classification. "History dictates we had a reasonable chance but the bottom line was [others] had bigger engines than us," he said. "It wasn't my day. I've used up my opportunities. Corsica was my race, now I'm a domestique for the GC guys."

Orica-GreenEdge pipped Mark Cavendish's Omega Pharma-QuickStep squad by a single second to win yesterday's team time trial and make it two stage wins in as many days.

The Australian outfit, whose bus crashed into the finish-line gantry to cause chaos on Stage 1, had won the first Tour stage in their history the previous day when Simon Gerrans sprinted to victory in Calvi, and they doubled up in Nice to put the 33-year-old former Team Sky rider into the yellow jersey.

Team Sky themselves settled for third place, three seconds back, after another gritty ride from Geraint Thomas on his cracked pelvis, the Welshman keeping up with his team-mates for 24 of the 25km before falling off the back. It may be the perfect scenario for Chris Froome, the Tour favourite, who has kept any time losses to an absolute minimum while not being required to defend the yellow jersey too early in the Tour.

Alberto Contador's Team Saxo-Tinkoff were fourth, nine seconds behind Orica GreenEdge, to keep the Spaniard in touch with Froome. Had they found a way to win, Ireland's Nicolas Roche, son of former Tour winner Stephen, would have taken the yellow jersey, but it was not to be.

Bakelants and his RadioShack-Leopard squad took to the course last and finished 29sec. back, good enough only for 11th as the Belgian's two-day stint in yellow came to an end.

Gerrans becomes only the sixth Australian to wear the yellow jersey, following Phil Anderson, Stuart O'Grady, Brad McGee, Robbie McEwen and Cadel Evans. Evans, the 2011 winner and an outside contender this year, finished ninth with his BMC squad, 26sec. back.

Gerrans is joined by two team-mates at the top of the new-look general classification, with the South African Daryl Impey second and the Swiss Michael Albasini third, both on the same time.

Omega Pharma-Quick Step's Michal Kwiatkowski, wearing the young rider's white jersey, and his team-mate, Sylvain Chavanel, are fourth and fifth, one second back. Norway's Edvald Boasson Hagen leads the Team Sky contingent, 3sec back, with Froome classed seventh and Richie Porte eighth.