EAST RUTHERFORD, N.J. – Kayvon Thibodeaux is in his second NFL season, but often speaks with the wizened authority of someone with far more experience. He did Sunday, after one of the most exasperating, disheartening and shocking losses in recent Giants history.

"You've just got to finish," Thibodeaux said. "NFL is a game of finishing, and they were able to execute at the end of the game and get enough points to win."

The Giants left rain-soaked MetLife Stadium with a staggering 13-10 overtime loss to the Jets, largely because of an inability to properly finish the game.

The defeat was exasperating because the Giants led for most of the second half, ran the ball for 203 yards and limited the Jets to 157 yards on their first 15 possessions. Disheartening because the Jets gained 104 yards on their final two series, including a four-play, 58-yard drive with no timeouts to tie the game at the end of regulation, and a 46-yard possession that included a 30-yard pass interference penalty to win the game in overtime. Shocking because, well, because they lost, which seemed almost impossible just a few minutes before Greg Zuerlien's game-deciding 33-yard field goal 3:51 into overtime.

"This one hurts," said coach Brian Daboll, who made a critical decision late in the fourth quarter.

"This one definitely stings," said running back Saquon Barkley. "… In that moment when everything's going your way, you feel like we can finish the game. We've just got to do a better job of finding a way to win that game."

The Giants played most of the game with Tommy DeVito at quarterback. Elevated from the practice squad for the third consecutive week because Daniel Jones was again sidelined with a neck injury, DeVito entered the game midway through the second quarter when Tyrod Taylor suffered a rib injury that necessitated a trip to the hospital.

DeVito is the first undrafted rookie quarterback to throw a pass for the Giants in the common draft era (since 1967). That does not include a 1987 strike-replacement game. He threw only seven passes, completing two, for minus-1 yard, but scored the Giants' only touchdown on a six-yard run in the third quarter.

"A lot of emotions," DeVito said. "Wish it would've ended better to fulfill those emotions, but the little kid in me is smiling right now that I got to play in an NFL game and really in a meaningful NFL game. I just wish the outcome would've been different."

Barkley tried to make it so by rushing for 128 yards on a career-high 36 carries.

"I told the guys at halftime we're going through 26 (Barkley)," Daboll said. "We're going to hand it off a bunch, we're going to play good defense, we're going to try to control the field position with our kicking game. We drove down there; it was a long drive there in the third quarter (that ended with DeVito's touchdown). Just kind of play it a certain way to try to win the game, and it just didn't work out."

Graham Gano's 31-yard field just 2:53 into the game was the Giants' only other score. Gano was wide left on 47- and 35-yard attempts.

The Jets scored on Breece Hall's 50-yard catch-and-run on a pass form Zach Wilson late in the first quarter and two Zeurlein field goals, including a game-tying 35-yarder as time expired in the fourth quarter.

The sequence that led to the kick began with 28 seconds remaining and the Giants facing a fourth-and-one at the Jets' 17-yard line. A handoff and the potential for a game-clinching first down seemed possible. Daboll opted for a 35-yard field goal attempt that would have given the Giants a six-point lead. But Gano missed the critical try.

Wilson quickly threw a 29-yard pass to Garrett Wilson. Thibodeaux was flagged for being offside. The Jets declined the penalty, but the infraction stopped the clock. Wilson followed immediately with another 29-yarder, to Allen Lazard. After spiking the ball with one second left, Zuerlein tied the game.

"Kick a field goal there, and they have 24 seconds with no timeouts, and they need a touchdown," Daboll said. "So, counted on making the field goal, and then they'd have 24 seconds with no timeouts, still have to drive it the length, and our defense was playing well all game. That's why I made the decision.

"It's a decision that we made to try to kick a field goal with Graham. Our defense was - they were like, 0-for-12 on third down. They were playing well. That's the decision we made. It didn't work out."

Was Barkley hoping to get the ball?

"It's fourth-and-one, I could sit here and be like, 'Oh, I want the ball in that situation,'" Barkley said. "But we've got nothing but trust in Graham, and we're going to continue to have trust in Graham. To be honest, I could have gotten the first down the play before. I've got to drive my feet a little more, or some other back could find a way to get a first down. You could sit here and pick and choose, oh the fourth-and-one, that decision or what should we have done there or not. You could make that the play, but there are so many plays that go throughout a game that help with the decision of how the game turns out. Just got to be better, all of us."

It likely would have been moot had Gano kicked the field goal.

"One hundred percent, if I make those kicks, we win the game," Gano said. "It's frustrating. I care about this team, the fans, I put a lot of work into this. It sucks, it sucks that I let everybody down. You can put it straight on me; there is nobody else honestly. This one is on me for sure.

"I have no excuses. That's not who I am. I'm sure some people want me to sit up here and make excuses, I've got none. I've got to play better. It's frustrating, I know the team played well. I just didn't. I've got to play better."

The Giants won the overtime coin toss but punted for the 13^th time in the game, giving the Jets the ball at their own 39.

On third-and-five from the Giants' 45-yard line, Wilson threw deep to wide receiver Malik Taylor, who was playing his first game of the season after being elevated from the practice squad Saturday. As Taylor tried to catch the ball, Adoree' Jackson ran into him, a 30-yard penalty that advanced the ball to the Giants' 15. Zuerlein then came on for the final dagger.

"Every loss is disappointing," Daboll said.

But the sting of this one will linger for a while.