Rangers goaltender Igor Shesterkin reacts after allowing the winning goal...

Rangers goaltender Igor Shesterkin reacts after allowing the winning goal on a shot by Colorado Avalanche defenseman Devon Toews in overtime of an NHL game on Tuesday in Denver. Credit: AP/David Zalubowski

DENVER — The look on Adam Fox’s face in the postgame locker room sent a clear message that of all the losses the Rangers have had this season, this one might have been the most frustrating.

The Rangers were within seconds of beating the Colorado Avalanche on Tuesday and stretching their win streak to three. But with the Avs’ goalie pulled for an extra skater, Artturi Lehkonen’s goal with 1:13 left in regulation forced overtime, and then, after the Rangers got a power play in the overtime but failed to score the winner, former Islander Devon Toews made them pay when he banged in a pass from Nathan MacKinnon with 36.1 seconds left in the OT to deal the Rangers a painful 3-2 loss.

“Good to the end, but we’ve got to get a win,’’ Fox said, through what seemed like tightly clenched teeth.

“I guess it’s the way you lose,’’ Fox said when asked why this loss was so much more frustrating than all of the others. “I mean, if you don’t play well, you don’t play well. But not coming away with two points in that game is definitely frustrating.’’

Having won two straight games, against the Devils and Vegas Golden Knights, the Rangers played a solid game, airtight defensively, and they outshot the Avalanche 29-26, and had more high-danger chances (12-10), according to Natural Stat Trick.

Goals from fourth-liners Sam Carrick and Adam Edstrom had them holding a 2-1 lead going into the third period, and their penalty kill, which has been so good all season, had snuffed out a Colorado power play that began at 6:57 of the third period.

At that point, it seemed as if the Rangers would escape.

But with the final minute approaching, the Rangers had a couple of chances to get the puck clear of the defensive zone, but couldn’t. Toews kept a puck in at the right point and passed to MacKinnon, who set up Mikko Rantanen for a shot that Igor Shesterkin stopped, but couldn’t control. The puck dropped to the ice and Lehkonen jammed it inside the near post to tie the game.

“The guys, I mean, they competed and did everything we wanted to do for 58 minutes,’’ coach Peter Laviolette said. “It’s really difficult walking away not getting that extra point. They tie it up, and even in overtime we had looks and chances to win the game and didn’t get it done. So that’s frustrating.’’

The Rangers’ lineup had been fortified by the return of forwards Chris Kreider and Filip Chytil, who missed four and two games, respectively, with upper-body injuries. Kreider was on the ice for the four-on-three power play the Rangers were given when Rantanen was sent off for an interference penalty 45 seconds into the extra session. He had two good looks at the goal but missed both shots, and the power play came up empty.

Shortly after it was over, Mika Zibanejad got a clean breakaway and made a good shot that Colorado goalie Mackenzie Blackwood made a glove save on, with 1:52 left.

Finally, the Avalanche won when they pinned the Rangers in their zone and MacKinnon found Toews alone in the right circle for a one-timer that got past Shesterkin before he could get over to cover the near post.

It was pointed out to Fox — who played his 400th career game — that taking three points out of a possible four after the first two games of the road trip, which concludes Thursday in Utah, is not a bad thing for a Rangers team that is 20-20-3, and has gone 4-1-2 since the start of the New Year to claw their way back into the playoff race.

“I think if, after the road trip, we come away with five out of six [points], I think you’re happy,’’ he said. “But, I mean, obviously talking right now, it stinks. It’s a game that should have definitely been two points. We played great hockey for 59 minutes and even still getting that power play in overtime. That’s another thing that just adds to the frustration.’’

The Rangers fell behind early on a goal by Parker Kelly at 4:53 of the first period, but Carrick’s third goal in the last six games, a shorthanded effort at 11:55 of the period, tied it, 1-1.

Carrick turned playmaker in the second period, setting up Edstrom’s second goal in two games at 9:59 to give the Rangers a 2-1 lead. Carrick picked up the puck after Colorado’s Casey Mittelstadt fumbled it away just above the left wing circle in the Rangers’ zone, and blew past defenseman Josh Manson at the point to set up a two-on-one with Edstrom.

Vincent Trocheck was 19-for-23 on faceoffs and played 26:01.

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