TAMPA, Fla. -- In Michel Therrien's eyes, his Montreal Canadiens lost their series to the Tampa Bay Lightning before Tuesday night.

They had opportunities to jump on Tampa Bay in Game 1 and to win Game 3. In falling behind three games to none, the Canadiens dug themselves too deep a hole and had nothing left in the tank to complete the comeback, losing 4-1 in Game 6 at Amalie Arena to be eliminated.

"I felt as a coach that physically and mentally we were drained," Therrien said. "So disappointed. I guess those things happen."

The Habs were the last Canadian-based team left in the playoffs. But for the 21st straight season, one will not win the Stanley Cup.

Tampa Bay will face either the New York Rangers or the Washington Capitals in the Eastern Conference final beginning Saturday. It's the Lightning's third trip to the conference final and first since 2011.

"I've always talked about 2011 was the most fun I've ever had playing this game," Lightning captain Steven Stamkos said. "We're getting right on that right now."

A second-round exit for Montreal looked likely after falling behind 3-0, but this team became the first in franchise history to even reach a sixth game when faced with that deficit. That was little consolation in the moments after the season ended.

"That's not really an excuse, though, because we put ourselves down 0-3," goaltender Carey Price said. "It is what it is."

For the first time in the second-round series the Habs were outshot, this time 28-19, and they weren't close for the first time since a 6-2 blowout loss in Game 2. Price stopped 24 of the 27 shots he faced and took responsibility for his team being done.

But a lack of offence actually doomed the Habs, as Max Pacioretty's goal late in the third period was more of a last gasp than a chance to get back into the game. Tampa Bay's goals -- two by Nikita Kucherov and one each from Stamkos and Ondrej Palat put Montreal in another hole too deep to climb out of, and Kucherov's empty-netter sealed it.

There were chances early on, but no adequate response to what Therrien called the Lightning's best game of the series.

"You can't afford to have passengers, everybody has to be a leader, and I don't think we had enough," defenceman P.K. Subban said. "I don't think we did enough to beat a good hockey team. We knew they were going to come out with their best effort tonight and we didn't match it."

The Habs finished the season with just three victories in 12 games against the Lightning, whom they swept out of last year's playoffs.

"I feel like we played a good series," said centre Tomas Plekanec, whose turnover led to Kucherov's first goal. "Although we lost all those games in the regular season, we played really good games. Personally I feel really better, but we just didn't put those pucks in."

Those weren't the only telling numbers. Montreal scored 13 goals in six games against Tampa Bay and in the playoffs as a whole went 2 for 36 on the power play.

When it mattered Tuesday night, they couldn't crack Lightning goaltender Ben Bishop, who made a big stop on Plekanec and got some help from the post behind him on a shot from Pierre-Alexandre Parenteau. Bishop finished with 18 saves to help the Lightning advance.

But the Habs didn't help themselves by missing opportunities.

"We could have scored goals, then they did, and since the second period we started pressing, forcing the plays too much," Plekanec said. "They were playing whatever they needed to and we were just pushing without any support, any other plays that we wanted to."

At one point Tampa Bay veteran Brenden Morrow levelled Alexei Emelin, and Alex Killorn crushed Subban. The Lightning beat and beat up the Habs to knock them out of the playoffs.

"It was a great group to be around," Pacioretty said. "It was a lot of fun overcoming a lot of adversity, proving a lot of people wrong that we were able to accomplish a lot. But we all had one goal in mind and we fell short."

Pacioretty scores a goal

Notes -- The Lightning were without winger Ryan Callahan, who had an emergency appendectomy Monday night. Jonathan Marchessault made his NHL playoff debut in place of Callahan, and Tampa Bay went with 11 forwards and seven defencemen.