Finnegan also admitted he was upset over talks about a contract extension, which was the personal issue he mentioned while defending himself Sunday on Twitter before returning to work.
"It has been nothing but a distraction to the team that was not needed," Finnegan said, according to The Tennessean. "When I was talking with my agent, because I wasn't happy with some of the things said, I let the emotions get the best of me and I had to take a step back personally and regroup.
"I took the negotiations personally, and I shouldn't have, and it affected everyone in the community and the team, and I deeply regret that. ... I want to be here long-term."
Finnegan left camp Friday night, and he missed Saturday's practice, which capped the opening week of camp. Titans general manager Mike Reinfeldt said after that session the team was surprised Finnegan had left, considering they were in talks about a new deal and, after practice Friday, had received a counterproposal from the cornerback's agent.
Finnegan said Monday that he was upset by what was said in the talks, and he wanted to head home to talk with his wife before his next move. His departure worried some teammates, who called to check on him.
"Was it wrong? Absolutely," said Finnegan, who'll make more than $3.7 million in the final year of an extension that he signed in 2008. "But it was something that I needed to talk about with her. I wanted to sit down and have a game plan moving forward."
Finnegan started off his Monday comments by apologizing to reporters he had accused on Twitter of having the story wrong. He also said he had talked with head coach Mike Munchak.
"I apologized to him tremendously (and) just for wanting me here still is big, and I appreciate him," Finnegan said.
Munchak said Finnegan will be fined for missing the practice, though he wouldn't say how much. The NFL's new collective bargaining agreement allows players to be fined $30,000 for each day of camp missed.
"We feel we've got things under control, and we're ready to move forward, and like I said, he missed Saturday. He'll be accountable for his actions that day," Munchak said.
Asked if Finnegan would be punished further by the team, Munchak said no.
"He knows that's not the way to handle the situation in the future, and if something happens in the future, maybe it'll be different," he said. "But for now, I think we did what we needed to do and time to move forward."
Finnegan, a 2006 seventh-round pick, has started every game in which he has played since the start of the 2007 season. He was a Pro Bowl pick in 2008.
Finnegan has 13 career interceptions but had just two last season when the Titans went 6-10. Finnegan also was fined by the NFL a few times, the most notable being a $25,000 bill for a Nov. 28 fight with Houston Texans wide receiver Andre Johnson, who delivered most of the punches. Johnson also was fined $25,000.
But Finnegan was a key leader for the Titans during the NFL lockout, helping organize a two-day minicamp at a Nashville high school in June, along with other sessions. He said he knows he didn't play to his best in 2010 and is eager to improve.
Finnegan said he hopes he didn't hurt talks with the Titans and appreciates them reaching out to him, considering 22 other players also are in the final year of their deals.
And Finnegan's teammates have accepted his apology.
"That's all you can ask for from a guy when a mistake happens, when an incident happens to own up to it and not run from you guys and not run from us, and that's what he did," fullback Ahmard Hall said.
The Associated Press contributed to this report.