Tavares assisted on Matt Moulson's goal in the second period Saturday against Carolina, but New York (3-3-2) lost 4-3 after falling behind by three goals.
The Islanders are 1-3-1 in their last five -- all one-goal games.
"Right now I don't think there's too much to be happy about," said Tavares, who has four goals and six assists during a seven-game point streak. "It's not good enough to respond the way we did. We can't play like that again.
"We've got to be better in all the little things of the game. We didn't seem to (dictate the play) for 45, 50 minutes of that game. We have to realize it takes that effort, that consistency, that mindset, that focus every game ... and we haven't done that yet."
Coach Jack Capuano agreed.
"We have the skill and resiliency, but we have to play a full 60 minutes," he said.
The losses of Visnovsky and Grabner won't make things any easier. Visnovsky was placed on injured reserve Monday after suffering a concussion against the Hurricanes, and Grabner's illegal check to the head of Nathan Gerbe landed him a two-game suspension.
Thomas Hickey, who is Visnovsky's regular defensive partner, said each player simply needs to focus on their own game.
"I think everyone just needs to step up a little bit more," Hickey said. "Lubo was a big part of our offense, a big part of our defense, but I've played a little bit with every guy throughout the year so you just go out there and play defense. You don't worry about who you're playing with."
New York looks to snap out of its funk against Vancouver, which is making its fifth stop on a season-high seven-game road trip.
The Canucks (5-4-1) won the first two contests before falling 4-3 in a shootout against Pittsburgh on Saturday and 3-1 to Columbus on Sunday. Henrik Sedin scored in the second period against the Blue Jackets to snap Vancouver's seven-game drought without a power-play goal, but it couldn't generate many other chances.
"It was tough to get good opportunities," said Sedin, who extended his point streak to five. "A lot of shots were outside and we didn't have a lot of traffic (in front of the net). If you don't have guys penetrating and getting to those areas, it's going to be tough to score goals."
Vancouver outshot the Blue Jackets 38-29, but coach John Tortorella wasn't pleased with his club's lack of pressure.
"Don't let the shots fool you," Tortorella said. "I don't think we played enough in the areas (you have to) to score goals. It's just a matter of willingness."
Roberto Luongo, who was drafted with the No. 4 overall pick by the Islanders in 1997 and played his rookie season with the club, should be back in net after resting Sunday. He's 3-1-1 with a 2.25 goals-against average in his last five starts versus his former team.
Evgeni Nabokov, who is 9-2-0 with a 1.73 GAA in his last 11 against the Canucks, could be in net for New York.
These teams haven't met since Sedin and Moulson each scored in Vancouver's 4-1 home win Nov. 13, 2011.