Justin Tuck said, often, how much he wanted to end his NFL career with the Giants. That won’t happen, because the Giants clearly didn’t want Tuck as fervently as he wanted them. As promised, Tuck on Thursday gave the Giants a chance to match the two-year, $11 million offer he received from the Raiders. The Giants declined to do so. In fact, their offer was not even close to what the Raiders anteed up — coming in the two-year, $6 million range. And, just like that, a Giants staple, the defensive team captain, a leader in the locker room and a fixture in the community made his exit, trading Giants blue for the Silver and Black of the Raiders. Tuck took the high road when he spoke publicly after the signing, but privately he is “devastated” by the Giants offer and “heartbroken” he was forced out of New York because the Giants offer was not competitive, someone close to Tuck told The Post’s Steve Serby. “I absolutely did not see it coming,’’ Tuck said on a conference call. “It wasn’t necessarily on my radar at that point in time, but everything accelerated pretty quickly and I’m excited. I really am. Obviously, everyone knows the history of the Raiders, and I just want to be a part of the group that brings it back.” The Giants cannot be shocked by this, unless they completely misread the market. The money the Raiders gave Tuck was solid, but nothing that should have blown the Giants out of the water. That the Giants didn’t come close was a sure sign they did not value Tuck as much as he thought they should. They chose to make the re-signing of linebacker Jon Beason (three years, $19 million) much more of a priority. “Obviously, everyone knows I love the New York Giants and I appreciate nine years of my career being there, but I just wanted a new, fresh start,’’ Tuck said, “and I think Oakland is definitely a good place to be.’’ Actually, what Tuck wanted was for the Giants to up their offer so he could return for a 10th season.