NEW YORK — The Celtics fully realized following their frustrating 120-114 loss to the New York Knicks that they tried to cheat the game and didn’t get away with it.

They allowed the upstart Knicks to get anything they wanted offensively in the first half Tuesday.

And when they desperately needed stops down the stretch, they couldn’t do it.

A shorthanded Knicks team shot 72.2 percent in the fourth quarter and held off their rivals to force a tie for second place in the Atlantic Division.

The Celtics have now lost four games in a row and seem rather bewildered about any possible solutions. They have slipped defensively and simply can’t outscore opponents, not when they keep sending opponents to the free throw line or experience constant defensive breakdowns.

With Knicks leading scorer Carmelo Anthony missing all but 19 seconds of the second half with a sprained right ankle and prized rookie Kristaps Porzingis fouling out, the Celtics had every reason to steal this win.

But they couldn’t contain the duo of Arron Afflalo and Jerian Grant in the fourth quarter. The duo combined for 20 points in the final period and the Knicks went on an 11-5 run to take the lead for good.

The pivotal play occurred with 1:53 left when Evan Turner, who entered the game 8 for 51 from the 3-point line this season, missed another and his defender, Derrick Williams, leaked out for an uncontested dunk for a 110-107 lead.

Finally, with the Celtics scratching to come back, they played stellar defense but Amir Johnson bumped Grant dribbling with four seconds left on the shot clock. Grant sank two free throws with 31.4 seconds left for a 3-point lead.

“We started out bad and we gave a lot of their bench players confidence and they made some clutch shots late in the game,’’ forward Jae Crowder said. “We didn’t come through. We didn’t execute late. It’s disappointing man, I don’t really know what to say. We lost the game. It was set up for us to win. We can’t blame nobody but ourselves.’’

What infuriated the Celtics was that Afflalo especially was allowed to get the ball in his sweet spot about 12 feet from the basket and shoot his customary turnaround jumper. When the Celtics did try to double, he simply dribbled through and shot anyway.

The Celtics allowed the Knicks to shoot 55.3 percent in the second half with Anthony getting no shot attempts and Porzingis just six. The quartet of Afflalo, Grant, Williams, and Robin Lopez were 18 for 26 in the final two periods.

“I thought in the first half we didn’t have any pressure on the ball,’’ Celtics coach Brad Stevens said. “In the second, I thought those guys [Knicks] made plays. It’s the thing is you try your best to make it as difficult as possible, so the other team is not in a rhythm on the offensive end. The Knicks felt so good after the first half and that’s it’s hard not to think that basket is bigger than it is.’’

Isaiah Thomas scored a game-high 34, but just 3 in six fourth-quarter minutes.

It seemed the Celtics would escape New York with a win when Jared Sullinger completed a three-point play for a 102-99 lead with 5:12 left, the Celtics’ biggest advantage of the night.

But the defense betrayed them again when Afflalo followed with a layup, Williams a three-point play, and Porzingis a jumper in Johnson’s face.

The frustration level is high. The Celtics were streaking at 18-13 just 2½ weeks ago after consecutive wins over the Pistons and Knicks.

Now they have lost six of seven games, including defeats to the Nets and Lakers, as well as 21-point blown lead Sunday at Memphis. So it was shocking that they played so passively to start Tuesday, trailing, 59-49, at halftime with a combined 37 points from Anthony and Porzingis.

“I feel like right now everybody’s not on the same page,’’ Crowder said. “We’ve got to back to doing what we want to do, all five guys on the court. Every guys is going to have to hold their end of the stick, it’s not just one guy. It’s everybody.’’

Anthony scored 17 in the first 24 minutes but he sprained his right ankle in a collision with official Steven Anderson with 1:16 left in the half and immediately headed to the locker room. He played briefly in the third quarter before being ruled out. Porzingis played just eight minutes in the second half because of foul trouble, but the Celtics couldn’t capitalize.

When asked what the Celtics need to do improve defensively, Thomas said: “Pay attention to detail, what guys like to do. Making it tougher on guys. In that first quarter I think they scored 36 points. You’re not going to win games on the road like that.

“We’re not doing enough of the little things to win these games. Hopefully it will change.’’

Gary Washburn can be reached at gwashburn@globe.com. Follow him on Twitter @GwashburnGlobe.