The Canadiens' Jonathan Drouin scores past Islanders goaltender Thomas Greiss during...

The Canadiens' Jonathan Drouin scores past Islanders goaltender Thomas Greiss during the second period of a game Thursday in Montreal. Credit: AP/Paul Chiasson

MONTREAL — Islanders coach Barry Trotz needs to see more goals from his struggling squad. He’d also like to see more fight.

Among the disappointments in Thursday night’s 4-0 loss to the Canadiens at Bell Centre was a lack of response to Andrew Shaw’s perceived cheap shot on Islanders defenseman Scott Mayfield late in the third period.

“My biggest disappointment is he gets run and all our guys stand around,” Trotz said. “That’s not good, so that will be addressed.”

Coming off Tuesday’s 5-0 loss to the Bruins at NYCB Live’s Nassau Coliseum and playing their first game since losing valuable third-line center Valtteri Filppula for four weeks with an apparent left shoulder injury, the Islanders (42-25-7) were shut out in back-to-back games for the first time since Nov. 19-21, 2011.

They remain three points behind the Capitals in the Metropolitan Division with eight games remaining. The third-place Penguins matched the Islanders’ 91 points with a 2-1 shootout win at Nashville on Thursday night.

In short, the Islanders are picking the wrong time to have trouble raising their performances to the compete level needed for the intense playoff push.

“I thought our first period, we weren’t bad,” center Casey Cizikas said. “That second period was where it got away from us and we lost the game. We can’t fall asleep at this time of the year. It’s unacceptable.

“This time, it’s not ideal, but eight games, you can do a lot in eight games,” Cizikas added. “You can definitely turn the tide and find the momentum and build it to where we were at.”

Thomas Greiss was replaced by Robin Lehner (12 saves) after allowing four goals on 22 shots. Carey Price made 28 saves for his fourth shutout of the season and 44th of his career for the Canadiens (39-28-7), who are battling the Blue Jackets for the second wild-card spot in the Eastern Conference.

The Canadiens opened the second period with three goals in 8:19 to make it 4-0.

Mayfield was run over along the right boards in the Islanders’ zone at 15:04 of the third period. He left, bloodied, for the Islanders’ room, and while he did return to the bench, he did not return to the game.

Trotz did not have an update on Mayfield.

Islanders defenseman Thomas Hickey did level Brendan Gallagher and those two fought at 17:31. In the final minute, Matt Martin was involved in a fracas with Canadiens defenseman Brett Kulak and then Nate Thompson.

“You start to get a little sick feeling in your stomach when you see one of your guys get cheap-shotted,” Hickey said. “I think it’s just frustration boiling over and we’re going to bind together and get out of it. We were obviously frustrated all game.”

For Trotz, it was too little too late.

“[Hickey] responded with a good hit. That’s what you need,” he said. “I like that response. I didn’t like the response when Shaw ran one of our guys and we’re looking for pennies.”

Joel Armia trickled a power-play goal through Greiss’ pads with 5.6 seconds left in the first period after the Islanders were outshot 3-2 on back-to-back power plays, including 21 seconds of overlapping five-on-three play. The Islanders’ power play was 0-for-3 on Thursday and has one goal in 14 games.

Defenseman Shea Weber blasted one over Greiss’ far shoulder from the right circle to make it 2-0 at 1:03 of the second period. Jonathan Drouin finished off a passing sequence from Jesperi Kotkaniemi and Armia at the crease to make it 3-0 at 6:00. Jordan Weal’s redirection of Jordie Benn’s shot ended Greiss’ night at 8:19.

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