Steven Davis, Northern Ireland’s captain, said: “He didn’t deserve that. No one does.”

McAuley’s misfortune, grim as it was, should not overshadow Wales’s accomplishment. With Bale leading the way, Wales has become one of the best stories of the Euros. Playing in its first major tournament in 58 years, the Welsh finished first in Group B with victories over Russia and Slovakia.

Now, after Saturday’s victory, Wales is in the final eight, with a quarterfinal match against the winner of Sunday’s match between Hungary and Belgium.

“They made it difficult for us,” said Bale, who had scored in all three group stage games. “But we knew we had that moment of quality in us. We were just glad that it finally came.”

There were, frankly, few others, as the play on the field, surrounded by an atmosphere of raucous chanting and singing from two groups of fans just delighted to be there, did not match the electricity in the stands. Three completed passes in a row was an unusual sight. Midfield play was rocky and stunted. There was lots of long, hopeful passing with far, far too many balls skidding over the end line for goal kicks.

It was, some might say, a display of the worst kind of English soccer, although that description also fit in other ways. Other than the sunny, warm day weather, the feeling here Saturday was very British: 19 of the 22 players in the starting lineups play for clubs in Britain, and an English Premier League referee, Martin Atkinson, was assigned to the game.

At a cafe near the Parc des Princes a few hours before the match, a server approached several tables of fans of both teams and was summarily, but kindly, told, “No one in here speaks French today!”

Political talk, much of it focused on Britain’s vote last week to leave the European Union, was largely put aside, save for a brief “Remain!” chant from Northern Ireland’s fans early in the match. (A majority of voters in Wales cast ballots to leave the E.U., while Northern Ireland voted to stay.) It was a day for sports, an opportunity for both teams to turn an already memorable competition into something truly remarkable.

Wales last played in a major tournament in 1958 and had never played in the Euros; Northern Ireland last played in the World Cup 30 years ago and was in its maiden Euros as well.

That was why the ending stung so much. Northern Ireland defended well, largely containing Bale and his teammate Aaron Ramsey. They had a few chances and, as O’Neill said, certainly felt they deserved the chance to take the game to extra time.

Instead, there was Bale flashing toward the wing, the ball suddenly coming across and McAuley, with nowhere to go, tumbling into infamy as the red end of the stadium roared.

Nearly half an hour after the final whistle, Northern Ireland’s players returned to the field. They walked out together and stood in front of the Wales fans who had stayed in the stadium, still singing. O’Neill was inside at the news conference, but the players wanted to savor one last moment from this tournament, wanted to feel that feeling one more time.

McAuley did not stay behind, did not sulk. Instead, he stood in the middle of it all and nodded as the fans warmly chanted his name. When the players finally began to head back to the locker room, he lingered a bit longer. He did not want to leave.