There are the games you think you shouldn’t lose and the games you can’t bear to lose. On Thursday night, the Knicks were dealt the former. On Saturday night, they experienced the excruciating disappointment of the latter.

Carmelo Anthony’s potential game-winning three-pointer spun around the inside of the rim and popped out as time expired as the Knicks fell to the Phoenix Suns, 107-105, at Madison Square Garden.

“That was a tough one to digest,’’ Anthony said. “We got the play we wanted. We got the shot we wanted. We got the look we wanted. We got everything we wanted . . . I was just thinking the ball was in. You couldn’t ask for a better look.’’

And you couldn’t ask for a tougher ending for the Knicks, who have lost 13 of their last 16. Then add that they were coming off a three-point loss to the Wizards and have lost three of their last four by a total of six points.

“It did everything it was supposed to do but stay down,” Courtney Lee said of the shot. “From where I was standing, I thought it was down.”

“I thought it was going down,” Derrick Rose said. “He had a good look . . . It was a good shot.”

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The Knicks (19-26) erased a 12-point second-quarter deficit and led by five with a little less than three minutes left in the game but could never get comfortable against the third-worst team in the league, and it cost them dearly when it counted the most.

Devin Booker scored six points in the final 2 minutes, 19 seconds, including a go-ahead three-pointer with 31 seconds remaining.

Rose (26 points, five assists) missed a contested driving layup with 26 seconds left. By the time the Knicks got the ball back, there were 6.3 seconds remaining and the ball went to the logical choice. Anthony got a clean look, compliments of Ron Baker’s screen.

“Our time is going to come,” said coach Jeff Hornacek, who offered Anthony a conciliatory hug after the game. “Teams get in here, and I know they get fired up to play in New York, but they always seem to make these shots . . . I don’t know what to say.”

Anthony scored 31 points — none in the fourth quarter — and added seven rebounds and six assists.

Booker led the Suns with 26 points and Eric Bledsoe added 23. Tyson Chandler had 16 rebounds.

It was the second heartbreaker in a row for the Knicks, though this might’ve stung even more than the three-point loss to the Wizards on Thursday night.

That was the game in which Lee passed up a potential tying three-pointer in the final seconds because he was distracted by Wizards assistant coach Sidney Lowe, who had sidled up next to him on the court. Thinking Lowe was a Wizards defender, Lee dribbled away from him before throwing the ball away.

Lowe and the Wizards were fined by the NBA, and the league said the next day that Lowe should have received a technical foul.

“It’s tough,” Lee said. “It’s coming down to the last possession on a lot of these games we’re losing. I think the fourth quarter was our best defensive quarter. We need to find out ways to get stops earlier.”