The Avalanche, who earned the second wild card into the playoffs from the West, lost Game 7 3-2 at SAP Center on Wednesday.
Colorado advanced to the second round for the first time since 2008 but hasn't gone further since 2002, when it defeated the Sharks in seven games in the Conference Semifinals.
The Avalanche, two seasons removed from finishing in last place in the NHL, won the Western Conference First Round series in five games against the Calgary Flames.
"It's obviously nice to take a step as an organization," center Nathan MacKinnon said. "We felt, especially with how the East was shaking out and with the West as well, that we could have won the Cup this year. It's so disappointing. We truly felt that we could have won everything. It was up for grabs, it was the year of the upset."