Ilya Sorokin of the Islanders looks on after surrendering a goal...

Ilya Sorokin of the Islanders looks on after surrendering a goal against the Golden Knights in the second period at UBS Arena on Tuesday. Credit: Jim McIsaac

The Islanders had their many chances to go 2-for-2 under Patrick Roy. They didn’t get the result.

But the players and new coach all left UBS Arena brimming with optimism after Tuesday night’s 3-2 loss to defending Stanley Cup champion Vegas.

“They should be positive,” Roy said. “I am very positive. C’mon, 27-13 scoring chances? Sometimes the puck just doesn’t go in. We played a good game and we were just not rewarded with it. It would be a shame if we have our heads between our legs after a performance like this.”

The Islanders (20-16-11) held a 42-27 shot advantage and an 80-41 attempt advantage. But they could not find the third-period equalizer after Jean-Gabriel Pageau’s shorthanded goal at 9:26 of the final frame despite three power plays over the last 20 minutes.

Roy’s tenure opened with an emotional 3-2 overtime win against the visiting Stars on Sunday night, a little more than 24 hours after he replaced the fired Lane Lambert.

Next up: An emotional return to Montreal where he spent the first half of his Hall-of-Fame goaltending career, winning two Stanley Cups.

“We were better on our breakouts overall,” Roy said. “We cut down on our turnovers tonight. We still want to cut down. Offensively, we held onto the puck better. We moved the puck better. We had a lot of good offensive-zone time possession. We looked more like a team that was playing a good game. It was not as crappy as the last game. It was more organized.”

“There’s a lot of things to like,” Kyle Palmieri said. “We played well. Had a lot of good looks. Defensively, I thought we played well. Didn’t give up a ton. Barring a couple of mistakes, it’s a really solid hockey game from us tonight.”

Ilya Sorokin, making his 10th straight start and 15th straight appearance, faced just 16 shots through the first two periods, though Vegas brought a 3-1 lead into the third period.

Goalie Adin Hill made his first start for Vegas (28-14-6) since Dec. 17 after being sidelined with a lower-body injury. Vegas, which took the LIRR to UBS Arena from its Manhattan hotel, was coming off Monday night’s 6-5 overtime loss to the Devils to open their four-game road trip.

A displeased coach Bruce Cassidy said after that defeat he thought his team, “basically played a beer league game.”

Vegas scored twice in a 1:49 span in the second period to take a two-goal lead.

Sheldon Rempal scored his first of the season when he connected on a rising power-play wrister from the right circle — defenseman Scott Mayfield was in the penalty box for interference — to put Vegas ahead 2-1 at 7:18 on a shot Sorokin saw cleanly. Nicolas Roy made it 3-1 at 9:07, tapping in a rebound at the crease after defenseman Noah Dobson’s giveaway.

Nonetheless, Brock Nelson said he thought the Islanders “cleaned it up.”

“Defensively, we were quick,” said Nelson, who notched his 500th career point as he tied the game at 1-1 from the right circle at 3:35 of the second period with the Islanders skating six-on-five after a delayed interference call on defenseman Zach Whitecloud. “We brought pucks up. Our neutral zone was better. They didn’t generate as many rush chances. Definitely positives. But it hurts not getting rewarded for it.”

Nelson nearly tied it in the final minute as he poked at the puck at the right post with Sorokin pulled for an extra skater.

Ivan Barbashev’s tip of defenseman Alex Pietrangelo’s shot opened the scoring for Vegas at 11:52 of the first period after defenseman Adam Pelech’s attempted backhanded clear from the crease was intercepted.

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