Schleck finished second in the race and has repeatedly said the decision to give him the title felt like a hollow victory since he did not secure it on the grueling roads of France. Contador lost the title when sports' highest court in February rejected his story that contaminated meat caused the failed drug test.
"It is not the same as to take the jersey on a podium in the tour, you don't have the podium girls, everything around is different," Schleck said.
The jersey was handed over to the Luxembourger during Tuesday's ceremony, attended by Tour de France organizers. It came on the eve of the Tour de Luxembourg, a preparatory race for this year's Tour de France, which starts June 30.
"It is two years after but I will never forget this tour it has been a very good tour," Schleck said.
Contador, who also won the Tour in 2007 and '09, tested positive for clenbuterol during a Tour rest day in July 2010. He was still considered the winner when the Tour ended that year.
"I was standing second on the podium, then the Contador case came up," Schleck said. "It was not me who took the decision so naturally I move up and I win the tour."
The CAS verdict in Lausanne, Switzerland, was delivered 566 days after Contador cycled triumphantly along the Champs d'Elysees in Paris.
"The lag is too big" for Schleck to get his jersey only now, Tour de France manager Christian Prud'homme said. "Sports authorities must work on reducing this lag in case of cases just like this one," he said after the jersey was put on Schleck.
This year, Contador has already missed the Giro d'Italia because of looming suspension. He will also miss the Tour de France and the London Olympics, but can ride in the Spanish Vuelta, which begins Aug. 18.