They put more pressure on themselves to live up to their first-place seeding, and it showed in earlier-round wins over the No. 8 New York Islanders and No. 6 seed New York Rangers when their A game was fleeting.
And they were definitely the tighter team through the first three games of the Eastern Conference final against the No. 4 seed Ottawa Senators.
Something happened, however, when they went down 3-0 in their best-of-seven series with the Senators. Having the hockey world write them off seems to have lifted some of that pressure, and it showed in a tremendous effort in their Game 4 victory.
"I think everyone is a little more relaxed," Sabres centre Daniel Briere said Friday after practice. "We're playing with a little more confidence."
Confident smiles have replaced grinding teeth.
"I don't feel the players being tight," said Sabres head coach Lindy Ruff, although he disagreed with the President's Trophy being a burden.
"I think they're a confident group. Confident is just knowing you can do it. They know they can do it."
The Senators aren't wasting any time thinking about the Sabres mental state.
"I'm not concerned with how they're feeling and how they think their game and their attitude and mental (approach) is or really what's going on in their dressing room," Senators forward Antoine Vermette after Friday's practice in Ottawa.
Vermette said the Sens only focus is on what they need to do to win Game 5 on Saturday (CBC, 2 p.m. ET) and end the series.
"We're confident that when we have our A game and our attitude is right and our focus is at the right place, we like our chances," he said.
The Sabres are hoping a win in Game 5 will tighten the collars of their opponents, who have been reminded of their past playoff troubles after failing to complete the sweep.
"We're looking at Game 5, and I think we have as good a chance of winning that game as they do," said Briere.
The Sabres are feeding off the old 'us-against-the-world' mantra, knowing few people believe they can be the first NHL team in 33 years to come back from a 3-0 series deficit.
"We've heard a lot of rumours that it was over, but nobody has told us that it's officially over so we're still battling," said Briere. "We're going to fight all the way to the end."
The odds may be stacked against them but Sabres were a relaxed bunch on the ice at practice Friday and in the dressing room. They didn't look like a team down 3-1.
"I kind of chuckled to myself when I saw (Chris) Drury playing goal before Game 4 and Derek Roy playing goal after practice," said Ruff. "You can read that any way you want it, but they were doing their best just to stay loose and enjoy it."
Ruff himself seemed more relaxed Friday, which surely filters down to the players. That's the difference between finally winning a game after losing three in a row, pointed out Briere, who says players feel so lousy after a loss in the playoffs that it affects them in many ways.
"You won't feel good about yourself, you won't feel good about your team, there's just something about it that makes you not sleep at night," said Briere. "You come in the next day and everybody is grumpy. When you win, it's just a little easier to show up at the rink and go to work."
Briere said winning Game 4 renewed their sagging confidence, it reminded them that they can still make plays and ultimately still win games.
"A lot of people counted us out and still do, and it seems to be driving us," he said.
Only twice in NHL history has a team come back from a 3-0 deficit and not since the 1975 New York Islanders, but Ruff said his team has what it takes beat the odds.
"We're not an eighth seed and not a team that snuck into the playoffs," said Ruff. "We're a team that went out and had a very good season. We won 10 games in a row. We've put together real good streaks and we have to put one together again, and last game was a very good start for us."
With files from Chris Yzerman in Ottawa