It was a scene almost designed to show the folly of the N.F.L.’s first-down measurement system.

Late in the fourth quarter of the game between the Dallas Cowboys and the Oakland Raiders on Sunday, Dak Prescott barreled into his offensive line on a fourth-and-1 quarterback sneak.

As is often the case in such plays when the ball carrier is swallowed in a mass of large human bodies, it was difficult to tell precisely where the ball should be placed.

But officials made their best guess and brought the yardsticks out to measure. Even then it was too close to call with the naked eye, so a referee, Gene Steratore, used a folded piece of paper to see if it could slip between the ball and the yardstick.

When it touched the ball, Steratore signaled a first down. The Cowboys would go on to kick the game-winning field goal, keeping their playoff hopes alive and effectively ending Oakland’s.

While the N.F.L. has long been considered a game of inches, if not millimeters, the episode raised questions: Why are referees still relying on eyesight to determine where the ball is placed? Isn’t there technology that could accurately call first downs and goal-line plays? Couldn’t officials put an electronic chip in the ball the way they do in some other sports?

The N.F.L. has already put a chip in the ball. As of this season, each game ball has a nickel-size chip made by Zebra Technologies that gathers data on the speed and flight of the ball. The chips, which are used by coaches and analysts to evaluate player performance, weigh about 4 grams. The ball is about 400 grams.

The chips aren’t used by referees to spot the ball, which is a bigger technological challenge.

John Pollard, vice president for business development at Zebra, said “further development would be needed to tune the level of accuracy to support needs like first-down measurements and goal-line calls.”

The chips provide advanced data but aren’t designed to pinpoint the ball’s exact location, Brian McCarthy, an N.F.L. spokesman, said in an email on Monday.

They are accurate to within six inches of the ball, which wouldn’t help when the most contentious calls come down to much smaller distances.

“We are always looking for ways to responsibly incorporate the latest technology into all facets of the game,” he wrote. “For a number of years we have considered various potential first-down measurement technologies but have not found one to date that we were comfortable with to deploy.”

Other sports have used technology for years. The United States Open was the first major tennis tournament to use Hawk-Eye technology, in 2006, and it has largely won over traditionalists. Most tennis tournaments use it, though the French Open does not, and television viewers can rapidly see whether balls land in or out.

The World Cup began using GoalControl technology in the 2014 men’s tournament. Fourteen cameras monitor the goal line, and watches worn by referees flash the word “Goal” within a second of the ball crossing the line.

But the N.F.L. has challenges other sports don’t face. A Hawk-Eye spokesman told ESPN in 2015 that the cluster of players around first-down and goal-line plays could make its system useless because 25 percent of the ball must be clearly visible for it to work. Hawk-Eye did not respond to a message seeking comment.

For now, the human element will live on. Though some Raiders said they thought there was space between the paper and the yardstick, Steratore denied that and said the paper was used to back up his decision.

“Didn’t use the card to make the final decision,” he told a pool reporter. “The ball was touching the pole. I put the card in there, and as soon as it touched, it was nothing more than a reaffirmation.”

Correction: December 19, 2017

An earlier version of this article misstated the technology used to track tennis balls in some competitions. The Hawk-Eye system relies on cameras, not chips attached to tennis balls.