"I'm probably not going to say a whole lot," Schneider said. "My teammates played well enough to win, and we deserved to win that game. We scored six goals and should win going away. The difference tonight was in net, so the game speaks for itself."
Palmieri's third goal tied it 6-6 tie with Schneider pulled for a sixth attacker and eight seconds remaining in the third period.
The Lightning lost 4-1 at the New York Rangers on Tuesday.
"We played two teams with a nothing-to-lose mentality the past two nights, and in a way that's something we can adopt," said defenseman Kevin Shattenkirk, in his first season with Tampa Bay, which had an NHL-high 128 points last season. "I think it's a different season for a lot of these guys, including me. We're not going to be the team they were last year, and the sooner we start to come to grips with that, I think we'll get past the living-on-what-happened last year mentality, assuming that things are going to go our way."
Palat had given the Lightning a 6-5 lead with 3:57 left in the period.