The Flyers are 1-5 in shootouts this season and an NHL-worst 20-39 in their history.
Bryzgalov played well in the first 65 minutes and notched his 25th career shutout, but he struggled in the shootout. He is 0-4 in shootouts this season, having allowed eight goals on 10 shots.
"I think we play very well, but it's a bad taste in the mouth after losing in the shootout," said Bryzgalov, who suffered a loss while recording a shutout for the first time in his career. "Obviously, I've got to work on this kind of thing in the practice more."
The last time the Flyers were in a scoreless tie that reached a shootout was Dec. 6, 2005, when Antero Niittymaki and Calgary's Mikka Kiprusoff were the goalies. The Flyers won the shootout.
The Flyers' top line of Claude Giroux (6), Scott Hartnell (6), and Jaromir Jagr (4) combined for 16 of the Flyers' shots Tuesday.
Jagr, who was robbed on an early one-timer, said Nabokov was "reading the plays. He was there even before we tried to shoot. Even when we went give-and-go or a cross-ice pass, he was there. I don't know if he's that quick or he was reading it very well. He was good tonight."
"He made the saves that he had to, but we didn't put traffic in front of him," said Giroux, who would have been the third shooter had the shootout gone longer. "He likes to get his room. He challenged a lot of shots, and I think we kind of let him do whatever he wanted. I think we've got to do a better job of screening the goalie."
First periods have haunted the Flyers recently, so it was almost a moral victory that they were in a scoreless tie after the opening 20 minutes, outshooting the Islanders, 10-7.