Sullivan, known for his upbeat attitude, takes his team to New York to face the struggling Rangers at Madison Square Garden.
The loss left the Bruins with only a two-point lead over Ottawa -- which beat the Rangers on Saturday -- for second place in the Northeast Division. Boston had been in first place for much of the first two months of the season.
"I thought it was night and day," Sullivan said about the difference between both losses. "I thought we played much better. I thought we played smarter. The scoring chances that we gave up weren't as high-quality. And, I think, because we played smarter, we ended up getting some scoring chances ourselves.
"We had opportunities to score."
The Bruins could only capitalize on one, when Glen Murray scored his 11th of the season with a power-play goal midway through the third period. Despite outshooting its opponents 67-39 over the last two games, Boston has been outscored 7-1.
"We can't feel sorry for ourselves," Boston center Martin Lapointe said. "That's the last thing we need to do. We were down 2-0 and tried to come back. Guys put a lot of effort into it, but we didn't get the result. We've got to go back to practice tomorrow and take the positives out of the game and make sure we play hard."
Rookie goaltender Andrew Raycroft made his eighth straight start Saturday, stopping 23 shots as the Bruins killed all seven of Carolina's power plays. Murray's goal snapped an 0-for-17 streak with the man advantage for Boston, which is eighth in the NHL on the power play.
The Rangers, meanwhile, have alternated wins and losses in their last five games, but have dropped six of nine overall.
In Saturday's 3-1 loss to Ottawa, Darius Kasparaitis ended a 52-game goal drought 8:01 into the first period for a 1-0 lead, but New York went on to allow three unanswered goals.
Goalie Mike Dunham made 20 saves, but fell to 2-7-2 in his last 11 starts.