The Avalanche had an NHL-worst 48 points last season.
"It's got to be one of the best accomplishments in modern sports history," Colorado forward Nathan MacKinnon said. "We came in last by 20 points, we were the worst team in 25 years. We did the unthinkable. It's obviously a huge deal."
The Predators and Avalanche have never faced each other in the playoffs.
Nashville has qualified for the playoffs four straight seasons, and made the Stanley Cup Final last season, when it lost to the Pittsburgh Penguins in six games.
"It's definitely a lot of motivation," Josi said. "I think most guys you talked through throughout the summer, obviously there was a huge disappointment, but after a couple weeks everybody just wanted to get back to Nashville and get back going. Right from the beginning we were a motivated team. We definitely do not want to be in a position again like we were last year."
This is the first playoffs for Colorado since 2013-14.
"They've been a great team all season, but they went in as the eighth [seed] last year, and it just goes to show that once you get in it's a completely new season," Avalanche defenseman Mark Barberio said. "Again, it's going to be a lot of hard work but this group is definitely up for it."
NHL.com staff writer Tracey Myers and correspondents Robby Stanley and Rick Sadowski contributed to this report.