But Talansky surged past the favourites during the 131.5 km eighth stage from Megeve to Courchevel to win by 27 seconds.
"Moments like this make the sacrifices worthwhile," an emotional Talansky told reporters.
While Contador trailed in more than a minute behind Talansky in the final stage, Froome struggled to maintain contact and ended up finishing outside the top 10 in the general classification.
Froome's fellow Team Sky rider Mikel Nieve won Sunday's stage in three hours 20 minutes 29 seconds.
Froome said he had been suffering from a crash on stage six.
"I've felt completely blocked up through my front of quads since the crash and I've not been able to engage the same types of muscles that I used in the earlier stages," he said.
Looking ahead to the Tour de France, Froome added: "(Contador's) shown he's in great form ahead of the Tour though, and we're definitely going to have a battle on our hands in July."
Talansky produced a stunning late breakaway to cross the line in fourth, nine seconds behind Nieve.
(Reporting By Tom Hayward, editing by Pritha Sarkar and Martyn Herman)
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