The Avalanche were already without goalie Philipp Grubauer, center Nazem Kadri and forwards Colin Wilson and Matt Calvert; each has a lower-body injury.
"I think every team's going through it a little bit," Bednar said. "But you start racking them up with Grubauer, Kadri, Calvert, now Mikko, our other guys got to step up. It's a great opportunity.
"We have to find a way to carve out wins like we did early in the year. It's going to get tougher and tougher, but hopefully we can get those guys healthy and back to join our team as soon as possible and guys are going to get opportunities and callups, and [it's] more ice time for guys that have been here wanting more ice time. We'll see what they got."
Andre Burakovsky's power-play goal gave the Avalanche a 1-0 lead at 4:49 of the first period.
The Lightning took a 2-1 lead in the second period on goals from Killorn and Gaunce 16 seconds apart. Ondrej Palat passed across to Killorn in the left slot for a shot into an open net at 4:54; Gaunce, playing his second game this season, shot from the left point at 5:10 for his first goal.
"It means a lot," said Gaunce, who played in place of injured defenseman Braydon Coburn (undisclosed). "In the moment, you can't grasp the significance of it. As my career has gone on, I've taken notice of the things that have gone on, live in the moment. Something like that, I'm really proud of it."
Stamkos scored on a rebound of Brayden Point's shot to make it 3-1 at 13:43.
MacKinnon made it 3-2 at 18:26 when he skated into the slot and shot stick side after taking a drop pass from Gabriel Landeskog.
