The 34-year-old is the Ducks' all-time leader in games played with 988 - 12 games away from becoming the first player to play 1,000 contests with the franchise.
"It stings," Perry told TSN's Frank Seravalli. "How many guys have played 1,000 games with one team? Not many. I sit here and say, well, with some of the injuries, I would've already been there. I was so close."
Perry said the decision wasn't a complete surprise, but he admitted he was still caught off guard when the team broke the news.
"When I was told, I didn't expect that to come out of their mouths," Perry said. "I respect their decision. It's tough when you've been there for so long, it's all you know. But I don't have a bad word to say about the Ducks and how they've treated me over the years. Everyone in the organization was good to me."
Drafted 28th overall by the Ducks in 2003, Perry helped the franchise capture its first and only Stanley Cup in 2007 - and his current situation is motivating him to capture another championship.
"This has definitely lit a fire in me," Perry said. "I want to win again. I've felt that feeling at every level and I want to feel it again. I watch teams win the Stanley Cup every year and I see how much emotion comes up when they win."
Perry underwent knee surgery before the start of last season and did not rejoin the Ducks' lineup until February, ending the year with a career-low six goals and 10 points in 31 games. However, he recorded 17 goals and 49 points during a relatively healthy 2017-18 campaign.