EAST RUTHERFORD, N.J. (CBSNewYork) — Regardless of how the 2015 season turned out, Tom Coughlin is going out a winner.

Following a memorable 12-year run as Giants head coach, an era filled with incredible highs and more recent lows, an upbeat Coughlin said his thank-yous and goodbyes on Tuesday during a formal press conference at MetLife Stadium.

“For me to stand here as the 16th head coach of the Giants at the conclusion of a 12-year term, it’s quite an awesome experience, to say the least.” Coughlin said.

“We all bleed blue together.”

The two-time Super Bowl champion resigned Monday following a disappointing 6-10 season, the Giants’ fourth straight season without a playoff berth.

“In professional football, the goal is to win. We all know that. It’s a bottom-line profession,” Coughlin said. “We understand that completely. But my contention is … there’s a higher ground. There’s a greater purpose. That purpose is team. Championships are won by teams who love one another, who enjoy and respect one another and play for and support one another.”

Coughlin said players he coached are not just winners on the field, but also in life.

“We tried to develop the character of each man who walked through these doors,” he said. “Character is what endures. What has become extremely important to me, as I’ve grown in this position, is relationships. Relationships have become the primary objective in my career.”

MORE: Complete Coverage Of Coughlin’s Final Season With Big Blue

Coughlin directly addressed quarterback Eli Manning, who was in attendance with tears in his eyes.

“He’s extremely bright,” Coughlin said. “He’s extremely competitive. What you want your son to be made out of. He thinks he’s the reason (for Coughlin’s departure). He’s not the reason. Eli, it’s not you. It’s not you.”

Coughlin, who guided the Jacksonville Jaguars to two AFC championship game appearances in eight years prior to becoming the Giants’ head coach in 2004, went 102-90 with New York, and is 170-150 overall.

Reports have indicated Coughlin, who will turn 70 on Aug. 31, is not yet ready to retire from coaching altogether. If the right situation presents itself, he would return to the NFL, though it’s unknown at this time if he’s on any team’s radar.

“I’m not necessarily done with coaching,” Coughlin said.

Known initially as a fierce disciplinarian who in later years became more of a players’ coach, Coughlin led the Giants to five playoff appearances and won at least 10 games in a season four times. However, due to a variety of reasons, Big Blue went just 28-36 under Coughlin since winning the Super Bowl following the 2011 season.

Despite having a losing record most of the 2015 season, the Giants remained in contention for the NFC East title well into December, a feat some said was due to Coughlin’s experience and expertise. But ultimately, the Giants failed to win the division because they were hampered by the league’s worst defense and an offense that struggled at times to finish games. New York let six games slip away inside the final two minutes.

“When we lose, I lose,” he said. “When we win, you guys win. That’s the way it is.”

It’s not clear whether Coughlin resigned on his own or was forced out.

He left the press conference in a hurry and did not shake hands with co-owner John Mara on the way out, CBS2’s Otis Livingston reported. Whether it was an intentional snub is surely to be a source of debate. Giants Senior Vice President of Communications Pat Hanlon, however, said Coughlin was oblivious and had only one thing on his mind: to get out of there.

Earlier, Coughlin made a pointed comment when speaking about the Giants organization.

“They are football people,” he said. “And they don’t panic every time there is a missed third down — just after you go 6-10 twice,” he said with a smile.

Mara later spoke glowingly of Coughlin.

“He’s been everything you could ever ask for in a head coach, and we’ll always appreciate him for that,” Mara said. “He’s a Hall of Fame coach, a Hall of Fame person, and he leaves big shoes to fill.”

Mara said Coughlin agreed to help the Giants in some capacity heading forward.

“We want him to stay involved due to all he’s brought to this organization. I think back to all the times people had him dead and buried, including many in this room. I’m happy he persevered,” Mara said.

Mara said the discussion he and co-owner Steve Tisch had with Coughlin on Monday was not contentious.

“All good things come to an end at some point in time,” Mara said. “Coaches in this league that last 12 years are pretty rare. I can never begin to repay him for what he has done for this franchise.

Mara said the search for the Giants’ next head coach will be “extensive,” adding both offensive coordinator Ben McAdoo and defensive coordinator Steve Spagnuolo will be interviewed.

Mara confirmed earlier reports that general manager Jerry Reese’s job is safe, but said he expects the Giants to get back to being a force in the NFL sooner rather than later.

“We’ve lost some credibility as an organization,” Mara said, but added, “I still believe that Jerry Reese is the right guy to lead us going forward. Why do I believe that? Jerry put together two Super Bowl-winning teams. I would venture to say that if we were to poll all of you in this room two years ago about who the top general managers in the league are, every one of you in here would have him on your list. So now, two years later, after another bad season, do we want to throw all that out? I still think he’s capable of putting a great team together.”