New York Giants head coach Tom Coughlin holds up the Vince Lombardi Trophy a day after winning the Super Bowl in Indianapolis. (LUCY NICHOLSON/REUTERS)

—As the Super Bowl crowds poured out of town Monday, the New York Giants still were savoring one of the most improbable stretch runs to a championship in NFL history.

With two games left in the regular season, the Giants were a 7-7 team coming off their second loss of the season to the Washington Redskins. Coach Tom Coughlin’s job security again was being questioned and quarterback Eli Manning, who was having a brilliant season, didn’t seem destined to add more career-defining moments to his football resume any time soon.

But by the time Coughlin and Manning appeared here at the traditional Monday morning news conference for the Super Bowl’s winning coach and most valuable player, all the regular season strife was a fading memory. Manning and Coughlin are two-time champions with possible Hall of Fame credentials already in place, and the Giants are the first team with a 9-7 regular season record to win a Super Bowl title after their dramatic 21-17 triumph over the New England Patriots Sunday night.

“We never changed our attitude about what had to be accomplished and what we had to do,” Coughlin said. “This is a great statement to our players as well as to our mental toughness. That’s what you have to rely on. . . . We didn’t spend time thinking backward. We were always looking forward.”

The Giants won their final six games. They beat the New York Jets and Dallas Cowboys at the end of the regular season to capture the NFC East crown. They beat the fifth-seeded Atlanta Falcons, top-seeded Green Bay Packers and second-seeded San Francisco 49ers in the NFC playoffs to get to Indianapolis. Finally, they beat the Patriots in a rematch of the memorable Super Bowl four years ago that denied New England a perfect season.

All but forgotten now, and certainly forgiven, is a four-game losing streak that nearly ruined the Giants’ season, dropping their record from 6-2 to 6-6.

“For a while, as we were trying to get this thing organized, it didn’t look as if the end result would be this,” Coughlin said. “But because of their mental toughness, because they hung in there, because they continued to believe, because we continued to be in the hunt for the NFC East title, that was always there for us.”

Coughlin, at 65, became the oldest coach to win a Super Bowl. After some a bit of speculation during the week that a second Super Bowl victory might prompt him to make a triumphant exit from the sport, he said Monday he plans to return next season.

“I do have some ownership that has to give approval,” he said. “But I’m looking forward to it.”

The season began with Manning creating a stir when he said in a radio interview that he considered himself an elite quarterback. It ended with further justification of that contention. Manning became the fifth quarterback ever with multiple Super Bowl MVP awards.

“This business about elite quarterbacks, I think that question has come and gone,” Coughlin said. “I don’t think we’ll hear much about that again.”

Eli moved ahead of brother Peyton for the Manning family lead in Super Bowl titles, two to one. But he said: “This isn’t about bragging rights. This is a lot bigger.”

Manning said he’d spent time with Peyton and other family members after the game. He said Peyton, ever the quarterback, had questioned whether Eli had even seen a certain Patriots linebacker on a first-quarter touchdown throw to wide receiver Victor Cruz. Peyton also pointed out, Eli said, that the 38-yard pass to wideout Mario Manningham that ignited the Giants’ game-winning drive required both a superb throw and a superb catch.

“He was mad,” Eli Manning said. “He said everybody was talking about how great of a catch it was. He said it was a pretty good throw, also. It’s a brother looking out for me. He was proud of me and happy for me.”

The Giants’ winning touchdown came on a six-yard run by tailback Ahmad Bradshaw, a score New England purposely yielded as it tried to preserve time on the clock for the Patriots’ offense. The Giants hadn’t discussed what they would do if the Patriots used that tactic. Manning said it occurred to him leaving the huddle what might happen, and he did his best to urge Bradshaw to stop shy of the goal line when he saw the play unfold.

“I just yelled, ‘Don’t score! Don’t score!’” Manning said Monday. “Obviously he heard me.”

But he also said: “I think you have to score a touchdown in those circumstances" rather than working toward a final-play field goal attempt. Bradshaw tumbled into the end zone after trying to stop.

“Would I have orchestrated it differently? Perhaps,” Coughlin said. “You certainly don’t want to leave that much time on the clock. . . . [But] it turned out the right way.”

The Patriots were left to ponder a series of near-misses, including a Brady pass that bounced off the hands of wide receiver Wes Welker and the final Hail Mary that was batted around before it fell incomplete.

“We talk an awful lot throughout [about] finish, finish, finish,” Coughlin said Monday. “And the young man who won the MVP certainly put our team on his back many, many times and we finished in the fourth quarter with some kind of a score that would allow us to eventually win the game.”