Quinn was quoted in a GQ magazine interview he gave three months ago as saying, "We've had a lot of, I guess, luck, to put it simply."
"I regret the comments as they appeared in the article and I apologize if the comments that were in the article upset anyone," The Denver Post quoted Quinn as saying Tuesday. "I think they were taken in the wrong tone. Had I known at the time the direction the article was going to go I would not have participated in the interview at all.
"However, there's no one to blame but myself. I take full responsibility. I've reached out to Tim and he knows what I think of him as a player and a person. I hope my teammates know that I don't think this season was based upon luck.
"I think it was more based upon the fight each of our teammates had to continually battle and win games in the end. And Tim was very much instrumental in our success, especially coming down the stretch in the last minutes of games."
Quinn also was quoted as saying the way Tebow expresses his Christian faith -- an often-copied and parodied kneeling pose -- doesn't "seem very humble to me."
Quinn posted several Twitter messages Tuesday in which he said he was happy for Tebow, who he called "a great teammate."
Tebow led the Broncos to several stunning comeback victories this past season after former starter Kyle Orton got off to an ineffective start, and defeated the Pittsburgh Steelers in overtime in the playoffs. Quinn had appeared to be the No. 2 quarterback but was passed over for Tebow.