MONTREAL -- The New York Rangers may have found the desperation they needed by seeing what happens when they don’t have it.

The Rangers departed for home Wednesday, a day after squandering their first of up to three opportunities to advance to the Stanley Cup Final with a 7-4 loss in Game 5 of the Eastern Conference Final against the Montreal Canadiens.

The Rangers still have a 3-2 lead in the best-of-7 series, but if they want to avoid wasting their second chance to close it out, in Game 6 on Thursday at Madison Square Garden (8 p.m. ET; NBCSN, CBC, RDS), they will need to find a way to manufacture some of the desperation the Canadiens showed Tuesday.

"That's how we looked at the game [Tuesday], and it didn't work out the way we wanted," Rangers coach Alain Vigneault said Wednesday. "We didn't show up [in Game 5] saying we have three chances to move on to the next step. We wanted to end it; it didn't work. But we're in a position where we can try again [Thursday]."

Manufacturing desperation when it doesn't exist is one of the most difficult things a team has to do in the Stanley Cup Playoffs. Some call it a killer instinct, but teams that succeed in the playoffs often find a way to approach every game as if it's their last, especially once they've reached this stage of the tournament.

The Rangers historically have had trouble with that, needing seven games for each of their past five series victories dating to 2008, when they defeated the New Jersey Devils in five games in the first round of the playoffs.

"You've got to try to create it the best you can," Rangers center Brad Richards said. "But I think in this situation, you win a game you go to the Stanley Cup Final. It's a desperate time. You don't want to go back to a Game 7 where anything can happen. We want to get this done, and we did [in Game 5] too. … But we're going to have to be a lot better, and we will be.

"The opportunity in front of us should create all the desperation that we need."

If there is one player this problem of finding desperation applies to the most, it's goaltender Henrik Lundqvist.

When Lundqvist was pulled in Game 5 on Tuesday after allowing four goals on 19 shots, it was the fifth straight time he lost a playoff game when the Rangers could advance but did not face elimination; he was pulled in four of those games.

For his career, Lundqvist has a 2-5 record in that particular situation, with an .841 save percentage. That save percentage drops to .808 in his past five games in that setting, all losses, and the Rangers will be in that same scenario again Thursday at Madison Square Garden.

"He'll be fine," Rangers defenseman Marc Staal said. "It's the last concern of anyone on our team."

The Rangers feel somewhat responsible for Lundqvist's performance in Game 5, and he mentioned after the game that even though he was taking responsibility for his own performance, his team needed to play much better in front of him.

"I know there's a lot of focus on me," Lundqvist said after Game 5, "but I think we all have to step up here."

Defenseman Dan Girardi agreed his goaltender was left exposed by mistakes made in front of him far too often, and that will need to change in Game 6, he said.

"We didn't give him too much help, and obviously [Vigneault] felt that was the right move just to get him out of the game," he said. "We didn't feel great about that, but we couldn't just sit there and mope around about it. We had to do something about it. We did. We came back and tied it."

If Lundqvist's history in close-out games without fear of elimination could be of some concern, his history in elimination games more than makes up for it.

In 17 career playoff games where the Rangers could be eliminated, Lundqvist is 11-6 with a .944 save percentage, including 4-0 with a .970 save percentage in these playoffs.

So if Lundqvist is unable to reverse one trend in Game 6, the Rangers can hope he maintains another in Game 7.