Mika Zibanajead and Chris Kreider scored, while Henrik Lundqvist finished with 22 saves in the loss.
"Right now all you feel is disappointment and it's a numb feeling," Lundqvist said. "It's not a great feeling. You realize how much work and how many hours you put into this to put yourself in this spot to get this chance. You started in July, last summer, to start to train and to prepare. It was right there for us."
After scoring first in the first five games of the series, it was the Senators who found twine first in Game 6, starting with Mike Hoffman's tally just 4:27 into the contest. Hoffman got a piece of an Erik Karlsson shot that beat Lundqvist up high to give Ottawa just its third lead of the series.
The Senators would double their lead just over 10 minutes later when Mark Stone's wrist shot beat Lundqvist at 14:44 of the opening frame. The goal was challenged by Alain Vigneault for offside, but was deemed legal.
"We came out slow, it's as simple as that," said Ryan McDonagh. "We can't put ourselves in a hole, but we did and I don't know why. We were all pretty focused in here, saying the right things. But it's a difference between saying and doing, and that showed up on the ice."