The Sabres fell one goal shy of a comeback after trailing 5-2 during the second period.
Jeff Skinner scored two goals while Alex Tuch (1+3) and Tage Thompson (0+2) had multi-point nights.
"It took us a little bit too long to push back," Tuch said afterward. "I wish we had done it probably halfway through the first or in the second, but it's a learning process.
"Just trying to stay up, stay positive and keep pushing guys. I think guys in here are really hard on themselves. It's good to keep yourself accountable, but you also have to work and play your game and not let it get into your head."
Read more in last night's postgame report.
Video: Postgame Interview: Alex Tuch
Thompson enters tonight on a five-game point streak after tallying a pair of assists against the Canucks. He leads the NHL in goals (10) and points (18) since October 29.
Tonight opens a run of three road games in Canada. After meeting the Senators, the Sabres play in Toronto on Saturday and in Montreal next Tuesday.
The Sabres are 3-3-0 on the road this season, having taken three of four games on a trip in Alberta and the Pacific Northwest in October before losing back-to-back, tightly contested games at Carolina and Tampa Bay earlier this month. Those losses marked the start of their current winless streak, which continued with an 0-4-0 homestand.
"We'll push through it," Granato said. "They learn from their mistakes, this group. They'll learn from this. This will make them better, but it doesn't lessen any disappointment.
"These are games that were right there, so you should have the expectation to win, and with the expectation to win, you should have that determination right at puck drop at 7 o'clock."
Video: Postgame Press Conference: Don Granato
The Senators have struggled to start the season after a summer of roster splashes, including the acquisitions of forwards Alex DeBrincat and Claude Giroux and goaltender Cam Talbot.
They are 2-7-1 in their last 10 games and have dropped five straight at home following a 4-2 loss to the Islanders on Monday. They are currently without their ice time leader in defenseman Thomas Chabot and their leading returning goal scorer in Joshua Norris, both of whom are out with injuries.
Giroux enters tonight on a nine-game point streak. He is tied with rookie forward Shane Pinto for the team lead with eight goals this season.
The Sabres defeated the Senators 4-1 on opening night at KeyBank Center. Victor Olofsson scored a pair of empty-net goals while JJ Peterka and Rasmus Dahlin also found the back of the net.
Tonight will be the second of four meetings between the Sabres and Senators this season, who will meet next in Ottawa on New Year's Day.