The forward scored an NHL career-high 23 goals in 66 games this season, but two in the final 29. He would have become a restricted free agent had he been qualified.
"All I will say about the situation is that Anthony chose to represent himself," Dorion said. "We told him from Day One that it's not always easy to represent himself.
"We offered him a substantial raise over what he made last year and it's unfortunate we couldn't come to a contract agreement. We don't close the door on anything, but he will explore free agency."
Duclair was traded to the Senators by the Columbus Blue Jackets on Feb. 23, 2019 and signed a one-year contract worth $1.65 million June 17, 2019. He has scored 162 points (79 goals, 83 assists) in 353 NHL games with the Senators, Blue Jackets, Chicago Blackhawks, Arizona Coyotes and New York Rangers.
Duclair joins Edmonton Oilers forward Andreas Athanasiou and defenseman Matt Benning among players who did not receive a qualifying offer and will become unrestricted free agents Oct. 9. Others include forward Dominik Kahun (Buffalo Sabres), forward Mark Jankowski (Calgary Flames), forward Devin Shore (Blue Jackets), defenseman Mirco Mueller (New Jersey Devils), forward Dominik Simon (Pittsburgh Penguins), forward Frederik Gauthier (Toronto Maple Leafs), defenseman Troy Stecher (Vancouver Canucks), forward Nick Cousins (Vegas Golden Knights) and forward Travis Boyd (Washington Capitals).
The NHL salary cap will remain at $81.5 million next season.
Jankowski was selected by the Flames with the No. 21 pick in the 2012 NHL Draft. He scored 64 points (36 goals, 28 assists) in 208 games for Calgary.
"Mark's been here a long time," Flames GM Brad Treliving said. "I didn't draft Mark, but we came into here together. He's a good kid. He's a good player. We wish him all the very best, but we just felt where he was at on a qualifier, that this was a prudent decision for us and we wish him all the very best and thank him for all he's put in during his time here."
Gauthier scored 12 points (seven goals, five assists) in 61 games this season for Toronto, which selected him at No. 21 in the 2013 NHL Draft.
"Fred has been a part of the organization for a long time," Maple Leafs GM Kyle Dubas said. "We just felt as we learned more and more about those who were going to market, we were going to look for a bit of a change."
Stecher scored two goals for the Canucks in the Stanley Cup Playoffs, including the game-winner against the St. Louis Blues in Game 1 of the Western Conference First Round.
"I talked to Troy this afternoon and explained to him this is a business decision and it's a tough part of the business," Canucks GM Jim Benning said. "He's been an excellent player for us and he shows up and he works and competes hard every shift, every game. ... We'll see what happens here the next few days but maybe we circle back around with them and try to figure something out that's cheaper or we move on."
