The French city was regarded as the outsider in the contest to decide the 2018 hosts and garnered just seven of the 95 International Olympic Committee (IOC) member votes on offer to finish third behind Pyeongchang, South Korea, and Munich, Germany.
"We are very proud of what we did and we think we have contributed to the Olympic movement but we lost and this is extremely disappointing," a visibly distraught bid president, Charles Beigbeder, told Reuters.
"We were hoping to be selected but we congratulate Pyeongchang because they were great competition and we thank the IOC for having given us the opportunity to bid," he added.
Pernilla Wiberg, twice an Olympic Alpine skiing champion and a member of Annecy's bid, said that being an athlete would help her to cope with losing out to Pyeongchang.
"It's a competition and there is always one winner and those that come second. I think as an athlete we learn from an early stage how to lose and how to win and it is the same here," the Swede said.
"Now we celebrate with Pyeongchang. It's been an extraordinary journey for us and we've learnt a lot."