OTTAWA — The game-winner was a fluky goal, one that Alain Vigneault thought was preceded by an icing.

But the Rangers coach conceded that his team didn’t do enough to beat the Senators before that in Game 1 of the Eastern Conference semifinals.

With 4:11 left in regulation, Erik Karlsson’s sharp-angle shot from the right side bounced off Derek Stepan and inside Henrik Lundqvist’s right post to give the Senators a 2-1 victory Thursday night in Game 1 of their second-round Stanley Cup playoff series.

“We felt on their winning goal it should have been an icing,” Vigneault said. “When we looked at the [replay] angles we get, I think it should have been icing. But at the end of the day you’ve got to play, and do more than we did tonight to win.”

Ottawa coach Guy Boucher’s trapping system was on display at Canadian Tire Centre, and the Rangers wasted a superb 41-save performance by Lundqvist, who almost singlehandedly killed three power plays in the first period.

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When the Rangers did break through the clogged-up space between the blue lines, they had some scoring opportunities, particularly by Michael Grabner, but couldn’t get enough out of their special teams.

“Any loss stings, and we’re down one game now,” said Stepan. “When we got through there, we had some looks, but we’ll have to attack more as a group. We’ll make our adjustments and that’s going to be a key in this series. Any loss stings. We took too many penalties, we didn’t have our discipline, but 5 on 5, I didn’t hate our game.”

The task for the Rangers in Game 2 tomorrow afternoon here is to break that system and defend much better.

After Lundqvist made 21 saves in the scoreless first period that included three power plays, the Rangers took a 1-0 lead in the second at 7:10 on a power play when Ryan McDonagh’s wrister from the left point went past a screen by Kreider to beat Anderson.

The Rangers got the man-advantage after Cody Ceci tripped Grabner. Grabner, who gave the Senators fits with his speed all night, beat Ceci to the puck, forcing the defenseman to trip him

Craig Anderson (34 saves) stopped Mika Zibanejad’s backhander in close off a rush. Grabner tried a jam in at the same post and another good play by Zibanejad to get a backhand off was stopped.

With 2:23 to go in the period, Brady Skjei was sent off for holding Tommy Wingels. The Senators were 0-for-3 on power plays with nine shots but tied the game on the fourth. Kyle Turris fired a shot off Lundqvist’s shoulder, and Dzingel pounced on the rebound at 18:39.

“The special-team battles were one for four each, but they were a little better,” said Vigneault. “You’ve got to make the other team pay for their mistakes and we didn’t and it came back to bite us.”

In the third period, the chances were few and far between as mid-ice was filled with players swatting pucks away. Dzingel wound up from 17 feet on a rush down the left side and Lundqvist snared it with his glove at 6:17.

Anderson matched that when he got his glove on Chris Kreider’s rising shot, deflecting the puck high off the glass behind the net.

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“I think both teams are going to wish they capitalized more on their chances,” said McDonagh. “We do, and we could be a lot better in front of Henrik.”