When Cullen Jenkins signed with the Giants as a free agent before the 2013 season, he thought he was coming to a winner.

As he finished that three-year contract, though, the team compiled a 19-29 record during his tenure. And more glaringly, they have not been to the playoffs with Jenkins on the team.

“I wouldn’t have believed that at all,” Jenkins said this week when asked what he would have thought if told of that drought on the day he signed.

He has trouble believing it now, too, even after it happened.

“I look back and, it’s been a while since I won the Super Bowl with Green Bay,” he said of the 2010 season, after which he spent two years in Philadelphia before coming to the Giants. “I haven’t been back to the playoffs since.”

He’d obviously like to again. And he’d like to with the Giants. But as one of the team’s many free agents, a player who has 12 full NFL seasons on his resume, and will turn 35 later this month, that may not be up to him.

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“You don’t know,” Jenkins said of this offseason’s uncertainty that already has included a head coaching change. “That’s one of the things in this business, there are things you can control and things you can’t control. We don’t know what’s going to happen. You sit back and time will play everything out. You just move in whatever direction stuff goes in.”

Jenkins certainly did not seem like he is finished as a player. He played in all 16 games for the Giants, had three sacks and 26 tackles. That’s an improvement from last year when he had just 15 tackles and one sack in 12 games. It’s also close to his career averages of 27.7 tackles and 3.9 sacks.

“I feel like I still have more to give, to play more,” he said. “I made it out of the season in good health, so that’s a blessing. I’ll take a little time off, rest the body a little bit, and then go from there.”

As for his three disappointing Giants seasons, Jenkins said the key is to learn from the experience.

“There’s nothing you can do about things in the past now,” he said. “You wish things would have played out different, but they played out how they played out. Now you just have to move on. You have to learn from it and take those lessons and try not to repeat them going forward.”