Vokoun made 24 saves for his fourth shutout of the season and Rostislav Olesz scored twice in the Panthers' 3-0 victory Saturday.
"We knew they were missing key people," Vokoun said. "We knew we had to take advantage and I think we did."
Nathan Horton also scored for Florida.
The Senators dropped their third straight game.
"We can't feel sorry for ourselves, nobody's going to," Senators coach Cory Clouston said. "We've got to keep working hard and I thought our guys battled and obviously we're missing some offense, but we've got to somehow find it. It's not the way you want to go on a long road trip that's for sure."
Despite two early power-play opportunities, the Panthers managed just two shots on goal in the first period. The Senators had one shot on goal on their first power play and failed to get a shot on Tomas Vokoun in the second.
"Obviously, the power play is a big concern," Clouston said. "There's some different guys out there with the injuries that we have and somehow we have to manufacture some offense."
The Panthers managed to end the period with a 1-0 lead after Horton picked up a big rebound and beat Brian Elliott high to the glove side.
Things didn't get much better in the second as Elliott allowed two bad goals, reinforcing Ottawa's goaltending woes.
On the first, Elliott made a bad pass behind the net and never managed to get back in position -- giving Olesz the whole left side of the net. On the second, Elliott mishandled Olesz's wrist shot that then slipped into the net.
The Senators lost Jesse Winchester with what appears to be an injury to his right knee after a collision with Keith Ballard. Filip Kuba left early in the third period with an upper-body injury and didn't return.
The Senators were without RW Daniel Alfredsson (shoulder), C Jason Spezza (knee) and LW Milan Michalek (upper body). The Panthers were without LW Kenndal McArdle (arm), D Dmitry Kulikov (knee) and LW David Booth (concussion).