"I didn't see that one coming," Davis told ESPN.com on Friday. "I mean, I saw the trade and all. I figured they'd bring in [Yates] to compete for the No. 2 during camp. But they went another way. And there's nothing I can do about it."
Davis knew his fate was sealed based on his limited reps during Thursday's final day of minicamp. After practice, offensive coordinator Dirk Koetter walked Davis off the field and told him he needed to meet with general manager Thomas Dimitroff and head coach Mike Smith.
"They pretty much told me they brought [Yates] in to be the No. 2 and they're only going to carry two quarterbacks on the [53-man] roster," Davis said. "So, they just let me go. I guess I'm just the odd man out. ... I left on good terms, though. That's all I can do."
Davis joined the Falcons in 2012 as an undrafted free agent out of East Carolina. He made his NFL debut during last season's blowout loss at Tampa Bay, when he replaced Ryan but had to come out of the game after suffering a knee injury.
Although playing behind one of the league's top quarterbacks was a good spot, Davis said he never got complacent with his approach.
"I came in every day busting my ass," Davis said. "I was doing everything the right way.
"The only thing I thought was I wasn't going to get cut right now. I knew I had to compete for the job, but I thought I would be good through camp. I was no way being arrogant by saying, 'I'm already on the team.' I just had the feeling that, yes, I'm going to be in camp for the Falcons."
Regardless of how things ended, Davis appreciated the Falcons giving him an NFL opportunity in the first place.
"I'm very thankful for these guys putting me on the map," he said.
Davis credited Ryan for helping him grow as a quarterback and setting an example of how to be a true professional. The two were teammates in college as well, when Davis redshirted at Boston College during Ryan's senior campaign.
"Just being an overall leader, being consistent, being a pro on and off the field," Davis said of Ryan's influence. "Just being a blue-collar guy and representing the Falcons, representing your family, and representing yourself. Everything he does, that's what I want to be. That's the platform I'm trying to get on as far as being an NFL quarterback."
Davis now has to await the waiver system before becoming free to sign with any team. He should be in someone's camp in late July.
"For starters, I'm going to compete," Davis said of how he'd sell himself to another team. "That's the only thing I know, is to compete. I'm going to come in and work hard. I'm going to be the first person in the building and the last person to leave.
"I'm a leader by example. I'm not going to say I'm your vocal guy, but I can lead by example. And I'm just going to come and be the best player I can be and try to make the locker room stronger and help the team reach its goals."
The Falcons will enter training camp with four quarterbacks: Ryan, Yates, second-year player Sean Renfree and rookie Jeff Mathews.