ARLINGTON, Texas - What in the world was Terrance Williams thinking?

The Cowboys receiver caught a 14-yard pass on a play that began with 12 seconds remaining in the game, but instead of heading out of bounds at about the Giants’ 40 or so, he inexplicably remained inbounds, and time expired before Dallas could spike the ball. “It’s a well-practiced situation,” Cowboys coach Jason Garrett said of Williams’ errant decision. “His instinct took him inside.”

“Obviously, I should have just followed the rules and gotten out of bounds,” Williams said. “In my mind, I was trying to get a first down and then dive out of bounds, but it didn’t go as planned . . . Looking back, I’ll never do that again.”

What were the Giants thinking while he did that?

“I thought he was going out of bounds, but he cut back in,” said cornerback Dominique Rodgers-Cromartie, who was guarding the sideline. “He wasn’t going out of bounds.” DRC took the extra step of sitting on Williams for an extra tick, preventing the receiver from lining up for a final play.

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Safety Landon Collins said the Giants wanted to prevent the Cowboys from getting across midfield, which would have given Dan Bailey a chance to win it from roughly 57 yards. Bailey already had kicked 56- and 54-yarders with ease.

“He had a leg on him,” Collins said. “He’d been kicking it out of the house.”

Did Zak DeOssie get his cap back?

He did. The Giants’ special- teams captain wore an FDNY baseball cap to the coin toss, but it was stolen from his head by former President George W. Bush, who then doffed it to the crowd. “That’s going in the man cave,” DeOssie said.

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The long snapper suspected that Bush might have felt comfortable enough “borrowing” it because they both attended the same high school: Phillips Academy in Andover, Massachusetts. “That’s the third time we’ve talked about it,” DeOssie said. “I reminded him of it when I got my hat back. Small world.”

Besides the hat trick, how emotional was the entire pregame ceremony and the 15th anniversary of Sept. 11?

“It was definitely one of the most memorable anthems and coin tosses,” DeOssie said. A 100-yard American flag covered the field to chants of “U-S-A!” and the crowd of 92,867 at AT&T Stadium sang “The Star-Spangled Banner,’’ which was played on a trumpet. There also were several videos referencing 9/11 and the rebuilding that took place in lower Manhattan.

“This day is very special,” said defensive captain Jonathan Casillas, a New Jersey native. “There’s no way to put in words how special and how important this day is for the whole country. Being a New York team and 9/11 being a New York event, I’m pretty sure back home they are proud of us. We wanted to put on a great show not only for the states of New York and New Jersey but for the whole country.”

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What happened on Eli Manning’s interception?

Rookie receiver Sterling Shepard said it was completely his fault. He did not come back to the ball and Manning threw it straight to Brandon Carr. “I just have to clean up my play,” Shepard said. “It’s really frustrating because the margin for error is really small in this league.”

The margin for success is small, too, right?

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Shepard learned that when he skied in the corner of the end zone to catch his first NFL touchdown pass in the second quarter. “I saw the ball in the air and I knew it was going to be a bang-bang play,” he said. “I had to go up and go get it and I was able to come down with it.”

Shepard said that play was more rewarding because the knock on him as a draft pick was his lack of size (he’s listed at 5-10). “That was the biggest question: Can I play big?” he said. “I try to show that every time I step on the field.”

Shepard had one more touchdown catch than Dez Bryant, at least?

Barely. The Cowboys receiver went up and caught a pass against Collins in the third quarter and the play was ruled a touchdown on the field. Replays, however, showed that Collins was able to knock the ball loose as the two fell to the turf. “My hand went through the ball and the ball went to the ground,” said Collins, who came up from the play imploring Ben McAdoo to challenge the call (all scoring plays are reviewed anyway). “I knew it wasn’t a touchdown.”

He also knew he would be targeted when Bryant was lined up against him in the slot. “I knew it was going to be a deep route and he would sit down,” Collins said. “I knew it was coming at me.”

How many others came to Bryant?

Not many. The star receiver was held to one catch for eight yards on five targets. “I know he was frustrated,” Cowboys owner Jerry Jones said. “You have to give them credit. They covered pretty good for most of the day.”

Any big injuries to watch this week?

Linebacker J.T. Thomas left the game with a sprained left knee.