The Rangers trail the best-of-seven Eastern Conference final 3-2 after Wednesday's home loss to the Devils, setting the stage for a must-win Game Six on Friday in New Jersey to have any shot at reaching the Stanley Cup Final.
"The most important thing that happened last night after a pretty screwy start is that ... our mindset changed," Tortorella said.
"That's really important for our team. I think we were us last night for a lot of the game."
The Rangers were once again hurt by a poor first period as the Devils burned standout goalie Henrik Lundqvist with three goals from their first five shots to put New York in a 3-0 hole less than halfway through the first period.
But the Rangers roared back with a goal in the first period, another in the second and an equalizer just 17 seconds into the final stanza, dominating play until the Devils went ahead for good with less than five minutes to play.
"We found our game last night, and I think that was mostly a mindset," said Tortorella. "We played more on our toes. We played to who we are. We have to do that tomorrow."
The two games won by the Rangers in this series came on shutouts by Lundqvist, the favourite to win the Vezina Trophy as the NHL top goaltender.
Tortorella said he is confident Lundqvist, who set a career high in wins during the regular season and placed near the top in all major goaltending categories, would recover.
"He'll play his best game tomorrow night," Tortorella, a finalist for this year's Jack Adams Award for NHL coach of the year, said about Lundqvist.
The Rangers were in the same position in their first-round test against the Ottawa Senators and advanced by winning the last two games of that series. New York also needed seven games to conquer the Washington Capitals in the second round.
"It's a good group," said Tortorella, a sometimes surly leader who has turned soothing going into a do-or-die game.
"It's a group that stays with it. They showed that last night through a little adversity early on. So there's not a lot of panic there. They just go about their business and we're a pretty good hockey team."
The coach said he had no motivational tricks up his sleeve.
"I don't have to motivate the team," he said. "We're preparing to try to win one hockey game. We prepare as we always do. There's no magic. There are no special speakers coming in. There is none of that."