When their season ended, the Washington Wizards walked over to the Boston Celtics with white towels draped over their shoulders. The players from both teams hugged, their new bitter rivalry deferring to mutual respect. They had beat up each other enough, at least for one year.

In Game 7, the Celtics triumphed at TD Garden, 115-105, outlasting a Wizards team that didn’t have enough defense or balanced scoring when it mattered. And so the Wizards, who lived by the comeback this season, finally fell into a hole they couldn’t claw and climb out of. It was another one of those nights for a D.C. pro sports team — close, but only close enough to feel the blade slashing at the wound once more.

“Our guys battled,” Wizards Coach Scott Brooks said. “It’s what we’ve done all year. We never quit. But give those guys credit. They played well.”

When the Wizards are able to look back, they’ll realize they didn’t really lose the series in Game 7. They were defeated amid all their lapses in focus and herky-jerky play in the other three games they lost. Having to win a series clincher here, where the Celtics are now 19-4 all time in home Game 7s, was a predicament they could have avoided if they didn’t leave so much on the court so often. If the core of this team wants to advance past the second round, it must continue to mature and gain the missing consistency or grit or depth or whatever that has created this wall the Wizards haven’t penetrated during three postseason appearances over the past four years.

Wizards guard Bradley Beal, who scored 38 points, reacts late in Washington’s 115-105 loss at Boston in Game 7 on Monday night. (Jonathan Newton/The Washington Post)

For the city, the 19-year curse continues. The Wizards joined the Capitals, who lost in Game 7 last week, as the latest D.C. teams to come up short of a conference finals appearance. For just the Wizards, this marked the closest they had come to a conference finals berth since 1979, but their 38-year drought remains. This setback comes with several harsh facts attached, none worse than this reality: In the final 19 minutes, John Wall didn’t score, but Celtics reserve forward Kelly Olynyk had 14 points.

“It was unbelievable,” Olynyk said.

That’s one adjective for it.

You could consider this the beginning of a fresh Wizards run, but it’s hard to be certain. They know better than any team how stingy life is with guarantees. Yes, most of their core is young. They are years from their prime, in fact. Yes, this was the first season under Brooks, and he resurrected an underachiever and led perhaps the greatest in-season comeback in NBA history, turning a team that started 2-8 into a 49-33 squad that came about one quarter shy of the Eastern Conference finals.

But right now, there is disappointment. There is disappointment because the Wizards’ season didn’t have to end. Not here. Not on this night. But they’re still a little too unstable in some areas to pull through and play to the level of their talent.

“It’s not a satisfied season to me,” said Wall, who had 18 points, 11 assists and seven rebounds despite shooting just 8 for 23.

Celtics center Kelly Olynyk, left, talks with Wizards guard John Wall after Game 7. (Jonathan Newton/The Washington Post)

It was exactly the kind of Game 7 you would expect from these teams. It was played in spurts. The series was tight, but it wasn’t defined by great individual games. Six of the seven games were decided by double-digit margins. The Wizards and Celtics were good enough to run away from each other, but not for long. The trailing team always caught up. The dramatic swings made the series compelling in lieu of a string of classic, wire-to-wire competitions. It’s more indicative of what the two teams are — green and still developing — that they teeter so frequently.

Basketball is a game of spurts, but my goodness, this was the spurtiest series ever. Game 7 went according to chaos.

The Wizards led 55-53 at halftime. They opened their biggest lead, at 70-64, on two Otto Porter Jr. free throws with 6:52 remaining in the third quarter. But then they would fall victim to the final dramatic run of the series, a change of momentum that would end their season.

Boston outscored Washington 18-3 during a stretch that lasted from late in the third to early in the fourth quarter. Isaiah Thomas, who had 29 points and 12 assists, made all three of his three-pointers in the run. Boston took a 94-81 lead, its largest of the game. And Olynyk started his transformation from the goofy, hard-fouling instigator victimized by Kelly Oubre’s Game 4 shove to the series-closing hero. He came off the bench and scored 14 of his 26 points in the final period. That’s how the Wizards’ season died, with Olynyk’s ponytail flapping as he trotted back on defense after making open jumpers, with the fans chanting “Kelly! Kelly! Kelly!” in celebration.

Death by Olynyk? Blame it on the Wizards’ defense, again. Their season-long weakness — the inability to get stops consistently when the offense isn’t clicking — returned in the second half. The Celtics shot 58.5 percent after halftime, and they made 8 of 14 three-pointers.

“You can’t win games if you’re going to let them do things like that,” said Wizards center Marcin Gortat, who finished with 11 rebounds but made just two of six shots.

If not for Bradley Beal, who scored 24 of his 38 points in the second half, the Wizards would’ve been done after falling behind by 13 points. But they had one little burst left in them. However, with Wall missing his last 11 shots, the Wizards never got closer than four points.

So after 11 games against each other — four in the regular season and this seven-game test of mettle — the Celtics proved better by the slimmest of margins. They won the Eastern Conference semifinals, 4-3, and the season, 6-5. In a matchup in which the home team won every time, the Celtics played one more home game. And they made it count.

For more by Jerry Brewer, visit washingtonpost.com/brewer.